BSM and Swaps - Complete
Juliana Morales and Felipe Tejada
2024-05-29
TRM 2000-2024 -Analisis Financiero- Labortatio 1
Datos_TRM = read.table("C:/Users/Felipe/OneDrive - INSTITUTO TECNOLOGICO METROPOLITANO - ITM/Derivados Financieros/TRM/basetrm.txt", header = TRUE)
# Guardar el archivo como un archivo HTML
library(knitr)## Warning: package 'knitr' was built under R version 4.3.2# Convertir la tabla a HTML
html_TRM <- kable(Datos_TRM, format = "html")
# Guardar el código HTML en un archivo
write(html_TRM, "tabla_trm.html")
head(Datos_TRM)## Fecha TRM
## 1 1/01/2000 1873.77
## 2 2/01/2000 1873.77
## 3 3/01/2000 1873.77
## 4 4/01/2000 1874.35
## 5 5/01/2000 1895.97
## 6 6/01/2000 1912.69# Transformacion al formato de fecha adecuado
Datos_TRM[,"Fecha"]<-as.Date(Datos_TRM[,"Fecha"],format = "%d/%m/%Y")
class(Datos_TRM[,"Fecha"])## [1] "Date"Graficacion de datos del precio de la TRM 2000-2024
plot(Datos_TRM[,"Fecha"],Datos_TRM[,"TRM"], type = "l", col="skyblue", main = "Serie Historica TRM 2000 - 2024")
Acorde al grafico, se puede inferir que la serie de tiempo analizada de los precios históricos de la TRM desde los 2000 a la fecha del año 2024, presentan un comportamiento de variación irregular, es decir, son cambios en la serie de corto plazo que por su aleatoriedad son difíciles modelarlos para proyecciones futuras. Esto por ejemplo se observa que entre los 10 primeros años la serie presentaba una tendencia con con precios aleatorios decrecientes, pero a partir del 2010 al 2024 los precios de la TRM presentan históricamente un tendencia irregular creciente.
plot(Datos_TRM[-1,"Fecha"], diff(log(Datos_TRM[,"TRM"])), type = "l", col="pink",
main = "Serie Historica Rendimientos diarios de la TRM")
Se puede observar del grafico anterior que en la mayor parte de este se mantiene una volatilidad constante desde aproximadamente el año 2000 al 2009 lo que se concluye que tuvo una estabilidad en el mercado, en los años siguientes se observa que tiene cambios positivos lo que nos puede indicar que la moneda se esta fortaleciendo y creciendo en su valor. Un caso de este es en el 2020 ya que se presento una pandemia lo que ocasiono que todo el mercado creciera y así incrementaran los valores de los productos.
Distribución de frecuencias
hist(Datos_TRM[,"TRM"], breaks = 30, col="yellow", main = "Histograma de los Precios de la TRM", freq = FALSE)
La grafica nos muestra unas fluctuaciones en sus precios entre los valores de 1500 y 5000, en este rango de precios se mantuvo la TRM en los periodos 2000-2024,se puede observar que ha tenido un crecimiento de precios constante debido a cambios en la política y un aumento en la tasa de inflación, se puede diferenciar que entre el rango de precios de 1500 y 3000 en estos periodos fue el mayor constacia
Rtos_TRM<-diff(log(Datos_TRM[, "TRM"]))
hist(Rtos_TRM, breaks = 50, col = "brown", main = "Histograma de Rendimientos TRM",
freq = FALSE, xlim = c(-0.02,0.02))
Con el grafico anterior se puede inferir que los rendimientos de la TRM estuvieron entre un aproximado de -0,02 y 0.02 teniendo mayor constancia en los rendimientos cercanos a 0, evidenciando un alza en un rendimiento cercano a cero pero en una tendencia negativa esto en consecuencia a las volatilidades que presento la TRM en los diferentes años
Datos estadísticos de la TRM entre el periodo 2000 - 2024
max(Datos_TRM[,"TRM"])## [1] 5061.21min(Datos_TRM[,"TRM"])## [1] 1652.41print("Media de la TRM entre 2000 - 2024")## [1] "Media de la TRM entre 2000 - 2024"mean((Datos_TRM[,"TRM"]))## [1] 2660.824print("Desviacion Estandar de la TRM")## [1] "Desviacion Estandar de la TRM"sd((Datos_TRM[,"TRM"]))## [1] 762.3418En términos estadísticos se evidencia que el máximo valor alcanzado de este periodo de la TRM es de 5061,21 y por su parte el menor valor alcanzada es de 1652,41, evidenciando las volatilidades que se tuvieron. Por otra parte, el valor mas constante en estos periodos de la TRM fue de 2660,824 y una dispersión de los precios de la TRM de 762,34
# Es necesario el paquete de "moments" para identificar el sesgo y la curtosis
library(moments)print("Sesgo")## [1] "Sesgo"skewness(Datos_TRM[,"TRM"])## [1] 0.896888print("Curtosis")## [1] "Curtosis"kurtosis(Datos_TRM[,"TRM"])## [1] 3.041658Dado el valor del sesgo con su cercanía a uno se puede inferir que es un sistema de datos sesgado es decir que implica una desviación sistemática de la objetividad o imparcialidad. Adicionalmente, su valor de curtosis al ser un valor positivo de 3,041658 se infiere que tiene una concentración mayor alrededor de la media recalcando sus valores atípicos.
# Percentiles de los valores de la TRM (2000-2024)
quantile(Datos_TRM[,"TRM"],c(0.01,0.05,0.1,0.5,0.75,0.90,0.95,0.99))## 1% 5% 10% 50% 75% 90% 95% 99%
## 1762.380 1791.625 1838.275 2389.750 3054.020 3856.000 4093.180 4802.480Datos estadísticos de los rendimientos de la TRM
max(Rtos_TRM)## [1] 0.05930667min(Rtos_TRM)## [1] -0.05621935print("Media Rendimientos de la TRM")## [1] "Media Rendimientos de la TRM"mean(Rtos_TRM)## [1] 8.36742e-05print("Desviacion estandar de los Rendimientos de la TRM")## [1] "Desviacion estandar de los Rendimientos de la TRM"sd(Rtos_TRM)## [1] 0.005923667skewness(Rtos_TRM)## [1] 0.2697665print("Curtosis")## [1] "Curtosis"kurtosis(Rtos_TRM)## [1] 12.81127quantile(Rtos_TRM,c(0.01,0.05,0.1,0.5,0.75,0.90,0.95,0.99))## 1% 5% 10% 50% 75% 90%
## -0.016723469 -0.008985171 -0.005719345 0.000000000 0.001295553 0.005983632
## 95% 99%
## 0.009561866 0.019031630# Estimación de un intervalo de predicción del 90% para los rendimientos de la TRM
quantile(Rtos_TRM, c(0.05,0.95))## 5% 95%
## -0.008985171 0.009561866# ¿Qué probabilidad hay de tener una perdida mayor al 1% en un día?
breaks<-c(min(Rtos_TRM)-0.0000001,-0.01)
corte<-cut(Rtos_TRM,breaks)
tabla<-table(corte)
print(tabla)## corte
## (-0.0562,-0.01]
## 359probabilidad<-tabla/length(Rtos_TRM)
print(probabilidad)## corte
## (-0.0562,-0.01]
## 0.04072604Supuesto de normalidad
# En este caso, se utilizara el promedio aritmetico de los rendimientos de la TRM
hist(Rtos_TRM, breaks = 50, col = "cornsilk", main = "Histograma
de los rendiemientos", freq = FALSE, xlim = c(-0.02,0.02))
curve(dnorm(x,mean = mean(Rtos_TRM), sd = sd(Rtos_TRM)),-0.02,0.02, add = T,
col="cadetblue")
En la siguiente grafica podemos observar como los rendimientos han variado a lo largo del tiempo, tienen tendencia creciente debido a que estos han sido la mayoría positivos debido a cambios estacionales o situaciones sociales.
# Comparacion de cuantiles
qqnorm((Rtos_TRM),col="aquamarine")
qqline(Rtos_TRM)
# Comparación de percentiles empiricos con los normales teoricos
cuantiles<-c(0.01,0.025,0.05,0.1,0.25,0.40,0.45,0.5,0.75,0.9,0.95,0.975,0.99)
qnorm(cuantiles,mean = mean(Rtos_TRM),sd=sd(Rtos_TRM))## [1] -0.0136968356 -0.0115264995 -0.0096598907 -0.0075078103 -0.0039117784
## [6] -0.0014170696 -0.0006607018 0.0000836742 0.0040791268 0.0076751587
## [11] 0.0098272391 0.0116938478 0.0138641839quantile(Rtos_TRM, cuantiles)## 1% 2.5% 5% 10% 25% 40%
## -0.016723469 -0.012630315 -0.008985171 -0.005719345 -0.001425601 0.000000000
## 45% 50% 75% 90% 95% 97.5%
## 0.000000000 0.000000000 0.001295553 0.005983632 0.009561866 0.013183574
## 99%
## 0.019031630Aplicación de asignación de probabilidad bajo el supuesto de que los rendimientos de la TRM siguen una distribución normal
# Estimación de un intervalo de predicción del 90% para los rendimientos de la TRM
qnorm(c(0.05,0.95),mean = mean(Rtos_TRM),sd=sd(Rtos_TRM))## [1] -0.009659891 0.009827239# ¿Qué probabilidad hay de tener una perdida mayor al 1% en un dia?
pnorm(-0.01,mean =mean(Rtos_TRM),sd=sd(Rtos_TRM))## [1] 0.04435248Simulación de montecarlo
Numero_iteraciones=10000
TRM_SIMULADA=matrix(,3,Numero_iteraciones)
TRM_Inicial=Datos_TRM[length(Datos_TRM[,"TRM"]), "TRM"]
TRM_SIMULADA[1,]=TRM_Inicial
for(j in 1:Numero_iteraciones){
for(i in 2:3){
TRM_SIMULADA[i,j]=TRM_Inicial*exp(rnorm(1,mean = mean(Rtos_TRM),sd=sd(Rtos_TRM)))
}
}
matplot(TRM_SIMULADA, type ="l", col = "lightpink", main="TRM Simulada")
hist(TRM_SIMULADA[3,],15, main = "Histograma Simulacion TRM 21 de Febrero de 2024", col="aquamarine")
Transfromacion de datos para reconocer la tendencia de posiciones del mercado
TRM_SimuTrp<- t(TRM_SIMULADA)
St<-subset(TRM_SimuTrp, select = 3)
k<-subset(TRM_SimuTrp, select = 1)
largo<- ifelse(St > k, St-k,0)
corto<- ifelse(St < k, k-St,0)
largo_cant<-sum(largo != 0)
corto_cant<-sum(corto != 0)Posiciones porcentuales en compra de la TRM
Porcentaje_largo<-(largo_cant/10000)*100
print(Porcentaje_largo)## [1] 50.22Posiciones procentuales en venta de la TRM
Porcentaje_corto<-(corto_cant/10000)*100
print(Porcentaje_corto)## [1] 49.78Representación grafica
Comparacion <- data.frame(Posiciones = c("Posicion en largo/Compra","Posicion en corto/Venta" ),
Resultado = c(Porcentaje_largo,Porcentaje_corto))
total<-rep(100, nrow(Comparacion))
barplot(t(as.matrix(Comparacion[,-1])),col = c("gold","cadetblue"),legend.text = TRUE,args.legend = list(x="topright"),
names.arg = Comparacion$Posiciones,main = "Comparacion entre las Posiciones del Mercado de la TRM",
xlab = "Posiciones",ylab = "Porcentaje",ylim = c(0,50),beside = TRUE,width = 0.5)
abline(h=50, col="black", lty=2)
legend("topright", legend = c(Porcentaje_largo,Porcentaje_corto),col = c("gold","cadetblue"),lty = 1)
Tiempo = 1:10000
plot(Tiempo, largo,type = "l",col="blue", xlab = "Simulaciones", ylab = "Posiciones", main = "Largo vs Corto")
lines(Tiempo, corto, col="aquamarine")
legend("topright", legend = c("Largo", "Corto"),col = c("blue","aquamarine"),lty = 1)
¿Es necesario acortar la información teniendo en cuenta que la TRM ha variado tanto en 20 años? Sustente su respuesta con fundamentos financieros o económicos.
Teniendo en cuenta que la TRM presento altas volatilidades en este tiempo consideramos no necesario acortar la información de datos, ya que en estos veinticuatro años transcurridos evidenciamos la tendencia que presento la TRM presentando una secuencia en los últimos años positiva en ganancia, es decir, con la información dada las posiciones de compra/larga fue la mas conveniente para la inversión ante la TRM.
Condiciones a evaluar
¿Cual es la probabilidad de obtener una perdida de hasta un 3% en un dia?
Probabilidad_perdida<-pnorm(-0.03,mean =mean(Rtos_TRM),sd=sd(Rtos_TRM))
print(Probabilidad_perdida)## [1] 1.901571e-07¿Cual es la probabilidad de ganar hasta un 5% en un dia?
Probabilidad_ganacia<- 1 - pnorm(0.05,mean =mean(Rtos_TRM),sd=sd(Rtos_TRM))
print(Probabilidad_ganacia)## [1] 0La probabilidad de perder en un dia hasta el 3% es muy baja y por otro lado, la probabilidad de ganar en un dia hasta el 5% es nula, la TRM debido a sus volatilidades no indica rendimientos en un porcentaje tan elevado en un dia.
¿Si usted invierte 10.000.000 COP cual es la probabilidad de obtener perdidas entre -500.000 Y 500.000 COP en un día?
#Probabilidad:
Inversion = 10000000
Ganancia = 500000
Perdida = -500000
Proporcion_ganancia = Ganancia/Inversion
print(Proporcion_ganancia)## [1] 0.05La probabilidad dado los datos indicados de obtener perdidas es del 50%
Simulación Montecarlo del derivado de la TRM entre 5/9/2023 - 23/2/2024
Datos estadisticos del derivado de la TRM
# Derivado de la TRM entre 5/9/2023 - 23/2/2024
TRM_futuros = read.table("C:/Users/Felipe/OneDrive - INSTITUTO TECNOLOGICO METROPOLITANO - ITM/Derivados Financieros/TRM/furutostrm.txt", header = TRUE)
# Guardar el archivo como un archivo HTML
library(knitr)
# Convertir la tabla a HTML
html_TRM_futuros <- kable(TRM_futuros, format = "html")
# Guardar el código HTML en un archivo
write(html_TRM_futuros, "tabla_trm.html")
head(TRM_futuros)## Fecha Pcierre
## 1 5/9/2023 4269.00
## 2 6/9/2023 4269.95
## 3 7/9/2023 4228.60
## 4 8/9/2023 4205.56
## 5 11/9/2023 4170.10
## 6 12/9/2023 4156.60# Rendimientos del derivado
Rtos_futurosTRM<-diff(log(TRM_futuros[,"Pcierre"]))
# Valor promedio de los rendimientos
Media_futuro<- mean(Rtos_futurosTRM)
Media_futuro## [1] -0.0007339315# Desviacion de los rendimientos
desvi_futuro<- sd(Rtos_futurosTRM)
desvi_futuro## [1] 0.01170066Numero_iteraciones=10000
TRM_futuros_Simu=matrix(,90,Numero_iteraciones)
TRM_futuros_Inicial=TRM_futuros[length(TRM_futuros[,"Pcierre"]), "Pcierre"]
TRM_futuros_Simu[1,]=TRM_futuros_Inicial
for(j in 1:Numero_iteraciones){
for(i in 2:90){
TRM_futuros_Simu[i,j]=TRM_futuros_Inicial*exp(rnorm(1,mean = Media_futuro,sd=desvi_futuro))
}
}
FuturoTRM_SIMULADA_TRANS<-t(TRM_futuros_Simu)
matplot(TRM_futuros_Simu,type = "l", col = "aquamarine", main="Futuros TRM SIMULADA")
Variables
Numero_contratos = 10
Nominal_contrato = 50000
Precio_inicial = 4198
Exposicion_Total = Numero_contratos*Nominal_contrato*Precio_inicial
Exposicion_Contrato = Exposicion_Total/Numero_contratos
Garantia_Inicial = 0.35
Valor_garantia_inicial = Exposicion_Total*Garantia_Inicial
Valor_garantia_minima = Valor_garantia_inicial*0.18Liquidación del derivado (Futuros de la TRM)
Liq_futuros<-TRM_futuros
Diferencia<-diff((TRM_futuros[,"Pcierre"]))
Diferencia <- append(0, Diferencia)
Liq_futuros<-cbind(Liq_futuros,(Diferencia*Numero_contratos*Nominal_contrato))
colnames(Liq_futuros)<-c("Fecha","Pcierre","Liq_Diaria")
margen<-matrix()
ColumnaA<-matrix()
length(ColumnaA)## [1] 1Llamado_margen<-matrix()
for (i in 1:(nrow(Liq_futuros))) {
ColumnaA[1]=Valor_garantia_inicial
ColumnaA[i+1] <- ColumnaA[i] + Liq_futuros$Liq_Diaria[i+1]
Llamado_margen[i] <- if(ColumnaA[i]<Valor_garantia_minima){Valor_garantia_inicial-ColumnaA[i]}
else{0}
margen[i]<-ColumnaA[i]+Llamado_margen[i]
}
ColumnaA## [1] 734650000 735125000 714450000 702930000 685200000 678450000 663025000
## [8] 649800000 629650000 638150000 635350000 655950000 654325000 711150000
## [15] 707250000 737900000 724650000 714100000 757850000 789150000 816950000
## [22] 894150000 806750000 777830000 806375000 808500000 797150000 781600000
## [29] 774950000 789525000 745900000 707850000 719200000 684150000 642650000
## [36] 662150000 692650000 670650000 666650000 637450000 631450000 696400000
## [43] 700650000 663700000 687150000 699355000 669650000 621100000 633850000
## [50] 663950000 619300000 646325000 655050000 632025000 634900000 640300000
## [57] 611450000 600100000 590650000 605550000 592225000 555650000 563650000
## [64] 548000000 582000000 584600000 577950000 590950000 601550000 583550000
## [71] 569590000 581550000 588050000 606950000 580100000 565450000 586250000
## [78] 578375000 571000000 579235000 579650000 558550000 583150000 597650000
## [85] 587550000 595055000 590250000 571700000 569900000 572650000 568725000
## [92] 564150000 564600000 566680000 570825000 571650000 578650000 587975000
## [99] NALlamado_margen## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [39] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [77] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0margen<-na.omit(margen)
Liq_futuros<-cbind(Liq_futuros,margen,Llamado_margen,Diferencia)Un intervalo de predicción del 90% del valor de la cuenta de margen para dentro de un mes.
#Base un mes (30 dias)
head(Liq_futuros$margen,30)## [1] 734650000 735125000 714450000 702930000 685200000 678450000 663025000
## [8] 649800000 629650000 638150000 635350000 655950000 654325000 711150000
## [15] 707250000 737900000 724650000 714100000 757850000 789150000 816950000
## [22] 894150000 806750000 777830000 806375000 808500000 797150000 781600000
## [29] 774950000 789525000#Se calcula la probabilidad con un intervalo de prediccion del 90%
qnorm(c(0.10,0.90),mean = mean(head(Liq_futuros$margen,30)),sd=sd(head(Liq_futuros$margen,30)))## [1] 647285028 817573972La probabilidad de perder mas de 10.000.000 COP en un mes
Probabilidad_perder_porce <- 10000000/150000000
pnorm(-Probabilidad_perder_porce,mean =mean(Rtos_futurosTRM),sd=sd(Rtos_futurosTRM))## [1] 8.75492e-09Si el margen mínimo es de 130.000.000 COP ¿Cuál es la probabilidad de ser llamado al margen?
El margen minimo es de $130.000.000 la probabilidad de ser llamado al margen es de 0% debido a que el valor minimo del margen es de $647.285.028, si queremos ser llamados al margen la garantía minima debe ser menor a este.
TRM Analisis mediante MBG - Laboratorio 2
Datos_TRM = read.table("C:/Users/Felipe/OneDrive - INSTITUTO TECNOLOGICO METROPOLITANO - ITM/Derivados Financieros/TRM MBG/TRM_MBG.txt", header = TRUE)Se analiza la serie diaria del precio de la TRM desde 2000-01-31 hasta 2022-09-17
Se descargan los paquetes requeridos
options(warn = -1)
suppressPackageStartupMessages({
library(knitr)
library(moments)
library(magrittr)
library(plotly)
library(dplyr)
library(ggplot2)
library(stats)
})# Fijar la base de datos
attach(Datos_TRM)
names(Datos_TRM)## [1] "Fecha" "TRM"options(scipen = 999)Reconocemos la tendencia de los datos
plot(Datos_TRM[, "TRM"], type="l", col="blue")
• La tendencia de la TRM ha sido creciente durante el período de tiempo analizado.
Primera parte
media<-mean((Datos_TRM[,"TRM"]))
media_anualizada <- mean((Datos_TRM[,"TRM"])) * 252
desviacion_estandar <- sd((Datos_TRM[,"TRM"]))
cuantiles <- quantile(Datos_TRM[,"TRM"], c(0.01, 0.05, 0.1, 0.5, 0.75))
sesgo <- skewness(Datos_TRM[,"TRM"])
curtosis <- kurtosis(Datos_TRM[,"TRM"])
maximo_valor <- max(Datos_TRM[,"TRM"])
minimo_valor <- min(Datos_TRM[,"TRM"])
estadistica_descriptiva <- data.frame(
"Descripción" = c("Media", "Media anualizada", "Desviación estándar", "Cuantiles (1%, 5%, 10%, 50%, 75%)",
"Sesgo", "Curtosis", "Máximo valor", "Mínimo valor"),
"Valor" = c(media, media_anualizada, desviacion_estandar, paste(cuantiles, collapse = ", "),
sesgo, curtosis, maximo_valor, minimo_valor)
)
print(estadistica_descriptiva)## Descripción
## 1 Media
## 2 Media anualizada
## 3 Desviación estándar
## 4 Cuantiles (1%, 5%, 10%, 50%, 75%)
## 5 Sesgo
## 6 Curtosis
## 7 Máximo valor
## 8 Mínimo valor
## Valor
## 1 2553.40167430087
## 2 643457.221923819
## 3 643.276997400928
## 4 1761.485, 1789.54, 1830.77, 2345.47, 2954.1575
## 5 0.747889447812386
## 6 2.68518407398657
## 7 4627.46
## 8 1652.411- Análisis Descriptivo
- Media: La TRM promedio durante el período 2000-2022 fue de $2.553,40 COP por USD.
- Media anualizada: La TRM anualizada durante el período 2000-2022 fue de $643.457,22 COP por USD.
- Desviación estándar: La desviación estándar de la TRM fue de $643.2769 COP por USD, lo que significa que en promedio el precio de la TRM puede subir o bajar $643.2769 en un día.
- Máximo: El valor máximo de la TRM fue de $4627.46 COP por USD.
- Mínimo: El valor mínimo de la TRM fue de $1652.41 COP por USD.
Análisis de Autocorrelación:
La TRM tiene una autocorrelación positiva, lo que significa que los valores actuales de la TRM están correlacionados con los valores pasados.
- Sesgo: El sesgo de la TRM es de 0.7478894, lo que indica una asimetría hacia la derecha.
- Curtosis:La curtosis de la TRM es de 2.685184, indica una distribución más aplanada que la normal.
Análisis de Tendencias: Durante el período analizado, la Tasa Representativa del Mercado (TRM) ha mostrado una tendencia creciente.
Esta tendencia al alza de la TRM ha sido influenciada por una serie de factores tanto internos como externos
Factores Externos - Crecimiento de la moneda cambiaria (USD), impulsada por el crecimiento economico de Estados Unidos. - Los conflictos geopolíticos en las regiones productoras. - Eventos económicos globales, como la guerra en Ucrania o la crisis financiera de 2008 en los Estados Unidos. - La pandemia de COVID-19 en 2020
Factores internos -La inflación en Colombia ha superado la de los Estados Unidos en los últimos años. Cuando el Banco de la República emite más pesos para aumentar la oferta monetaria. -Colombia presenta un mayor deficit con respecto a de Estados Unidos
Estadísticas Descriptivas de los Retornos
print("Rendimiento de la TRM")## [1] "Rendimiento de la TRM"Rtos_TRM<-diff(log(Datos_TRM[, "TRM"]))media_Rto <- mean(Rtos_TRM)
desv_Rtos <- sd(Rtos_TRM) * sqrt(252)
sesgo_Rtos <- skewness(Rtos_TRM)
curtosis_Rtos <- kurtosis(Rtos_TRM)
vol_TRM <- sd(Rtos_TRM) * sqrt(252)
# Crear la tabla de datos
Rendimientos <- data.frame(
"Descripción" = c("Media de los retornos anualizada", "Desviación estándar anualizada",
"Sesgo", "Curtosis", "Volatilidad de la TRM"),
"Valor" = c(media_Rto, desv_Rtos, sesgo_Rtos, curtosis_Rtos, vol_TRM)
)
print(Rendimientos)## Descripción Valor
## 1 Media de los retornos anualizada 0.0001038896
## 2 Desviación estándar anualizada 0.0918160270
## 3 Sesgo 0.2649411282
## 4 Curtosis 13.8843844743
## 5 Volatilidad de la TRM 0.0918160270Grafica de los Retornos de la TRM en el tiempo analizado
plot(Rtos_TRM, type="l", col="red")
Cuantos miden los precios y los retornos
length((Datos_TRM[,"TRM"]))## [1] 8296length(Rtos_TRM)## [1] 82952- Calcule de manera teórica un intervalo de confianza al 95% sobre los posibles precios futuros de la TRM
quantile(Rtos_TRM, c(0.05,0.95))## 5% 95%
## -0.008534254 0.0093272933- Realizando una simulación MBG con S=Precio de la TRM del 17 de septiembre de 2022, y t=180, volatilidad = histórica de la serie, mu = histórica de la serie, iteraciones = 10000, de los posibles precios futuros.
t=5/12
delta_t<-1/252
N<-t/delta_t
M<-10000
S<-matrix(ncol = M,nrow = (N+1))
S[1,]<-4435.84
for (i in 1:M){
for (t in 2:(N+1)){
S[t,i]=S[(t-1),i]*exp((media_Rto-desv_Rtos^2/2)*delta_t+desv_Rtos*sqrt(delta_t)*rnorm(1))
}
}
matplot(S, type = "l")
Proyeccion de los posibles precios futuros
length((Datos_TRM[,"TRM"]))## [1] 8296N+1## [1] 106proyeccion1<-matrix(nrow =(8296+105), ncol=1)
proyeccion1[1:8296]<-Datos_TRM[,"TRM"]
matplot(proyeccion1, type="l",ylim =c(1000,6000))
proyeccion2<-matrix(nrow =(8296+105), ncol=M)
proyeccion2[8296:8401,]<-S
matlines(proyeccion2,type="l")
# Intervalo de confianza
alfa<-0.025
q1<-quantile(S[(N+1),],(alfa/2))
q2<-quantile(S[(N+1),],(1-alfa/2))
# Valores entre q1 y q2
valores_vector <- seq(q1, q2, length=100)Distribución Empírica de precios futuros
plot(density(S[N+1,]), ylab="", xlab="",
main="Distribución Empírica", lwd = 3)
abline(h = NULL, v =q1, col = 'cadetblue', lwd = 2)
abline(h = NULL, v =q2, col = 'gold', lwd = 2)
Estimación de un intervalo de predicción del 95% para los precios futuros de la TRM
precios_futuros <- proyeccion1[complete.cases(proyeccion1), ]
qnorm(c(0.05,1), mean = mean(precios_futuros), sd=sd(precios_futuros))## [1] 1495.305 Inf2. Segunda Parte
Una empresa exportadora que realizó crédito para ejercer una inversión empresarial el 17 de septiembre de 2022 con los siguientes criterios de pago por parte de su capitalizadora de inversión:
Monto de inversión: 1’790.000 USD -Tasa de interés:_ 10% AMV Cuotas: 24 Frecuencia de pago: Mensual
Fechas<- c("17/10/2022","17/11/2022","17/12/2022","17/01/2023","17/02/2023")
Pago_USD<- c(91738,90992,90246,89500,88754)
Frecuencia_Pagos <- data.frame(Fechas = Fechas, Pago_USD = Pago_USD)
print(Frecuencia_Pagos)## Fechas Pago_USD
## 1 17/10/2022 91738
## 2 17/11/2022 90992
## 3 17/12/2022 90246
## 4 17/01/2023 89500
## 5 17/02/2023 887542.1. Simulación
mu_anu<-mean((Datos_TRM[,"TRM"]))*252
sigma<-sd((Datos_TRM[,"TRM"]))*sqrt(252)
T= 5/12
delta_t=1/252
N=T/delta_t
M= 1000 # Numero de simulaciones
TRM= matrix(ncol=M, nrow = (N+1))
TRM[1,]=4435.84
for(i in 1:M){
for (T in 2:(N+1)){
TRM[T,i]=TRM[(T-1),i]*exp((media_Rto-desv_Rtos^2/2)*delta_t+desv_Rtos*sqrt(delta_t)*rnorm(1))
}
}
matplot(TRM, type = "l",
main = "Distribución",
xlab = "Tiempo",
ylab = "Precio")
Proyeccion1 = matrix(nrow = (8296 + 105), ncol = 1)
Proyeccion1[1: 8296] = Datos_TRM[,"TRM"]
matplot(Proyeccion1, type="l", ylim = c(1500, 7000))
title("Proyección")
lines(Proyeccion1, col = "black", type = "l")
proyeccion2<-matrix(nrow =(8296+105), ncol=M)
proyeccion2[8296:8401,]<-TRM
matlines(proyeccion2,type="l")
2.2 Simulación Montecarlo Flujo de caja total esperado cuota sin cobertura
# Pagos dado en el planteamiento incial
Cuotas_USD = c(91738,90992,90246,89500,88754)
Cuotas_COP=TRM[2,]*Cuotas_USD[1]
for(j in 2:length(Cuotas_USD)){
Cuotas_COP=rbind(Cuotas_COP,TRM[j+1,]*Cuotas_USD[j])
}
media_cuotas=vector()
volatilidad_cuotas=vector()
percentil_5_cuotas=vector()
percentil_95_cuotas=vector()
for(l in 1:5){
media_cuotas[l]=mean(TRM[l+1,]*Cuotas_USD[l])
volatilidad_cuotas[l]=sd(TRM[l+1,]*Cuotas_USD[l])
percentil_5_cuotas[l]=quantile(TRM[l+1,]*Cuotas_USD[l],0.05)
percentil_95_cuotas[l]=quantile(TRM[l+1,]*Cuotas_USD[l],0.95)
}
matplot(Cuotas_COP,type = "l", col="cornsilk", main="Estimado Cuotas en COP", ylab = "Valor Cuota", xlab = "Cuota")
lines(percentil_5_cuotas, col = "blue", type = "l")
lines(percentil_95_cuotas, col = "red", type = "l")
lines(media_cuotas, col = "black", type = "l")
legend("topright", legend = c( "Percentil 5", "Percentil 95", "Media"),
col = c("blue", "red", "black"), lty = 1)
print("Volatilidad de cada cuota en millones de COP")## [1] "Volatilidad de cada cuota en millones de COP"print(volatilidad_cuotas/1000000)## [1] 2.400274 3.326175 4.003740 4.666252 5.0520632.3 Simulación de Montecarlo de los pagos de cuotas con cobertura (70%)
Cobertura<-0.7
Precio_Entrega= 4500
Utilidad_POR_USD=TRM[-1,]-Precio_Entrega
matplot(Utilidad_POR_USD,type="l", col="bisque", main="Utilidad por USD", ylab = "Utilidad (USD)", xlab = "Fecha")
Utilidad_total=Utilidad_POR_USD[1,]*Cuotas_USD[1]*0.7
for(j in 2:length(Cuotas_USD)){
Utilidad_total=rbind(Utilidad_total,Utilidad_POR_USD[j,]*Cuotas_USD[j]*0.7)
}
matplot(Utilidad_total,type="l", col = "burlywood", main="Utilidad Total", ylab = "Utilidad (USD)", xlab = "Fecha")
Cuotas_COP_CON_C=Cuotas_COP-Utilidad_total
media_cuotas_COP_CON_C=vector()
volatilidad_cuotas_COP_CON_C=vector()
percentil_5_cuotas_COP_CON_C=vector()
percentil_95_cuotas_COP_CON_C=vector()
for(l in 1:5){
media_cuotas_COP_CON_C[l]=mean(Cuotas_COP_CON_C[l,])
volatilidad_cuotas_COP_CON_C[l]=sd(Cuotas_COP_CON_C[l,])
percentil_5_cuotas_COP_CON_C[l]=quantile(Cuotas_COP_CON_C[l,],0.05)
percentil_95_cuotas_COP_CON_C[l]=quantile(Cuotas_COP_CON_C[l,],0.95)
}
matplot(Cuotas_COP_CON_C,type = "l", col="#FFF8DC", main="Estimado Cuotas en COP", ylab = "Valor Cuota", xlab = "cuota")
lines(percentil_5_cuotas_COP_CON_C, col = "blue", type = "l")
lines(percentil_95_cuotas_COP_CON_C, col = "red", type = "l")
lines(media_cuotas_COP_CON_C, col = "black", type = "l")
legend("topright", legend = c("Percentil 5", "Percentil 95", "Media"),
col = c("blue", "red", "black"), lty = 1)
print("Volatilidad de cada cuota con cobertura en millones de COP")## [1] "Volatilidad de cada cuota con cobertura en millones de COP"print(volatilidad_cuotas_COP_CON_C/1000000)## [1] 0.7200822 0.9978525 1.2011220 1.3998756 1.51561902.4 Beneficios reales de las series
Beneficio real sin cobertura
fecha <- c("17/10/2022", "17/11/2022", "17/12/2022", "17/01/2023", "17/02/2023")
valores_TRM <- c(4636.83, 4922.70, 4802.48, 4693.99, 4966.33)
# Crear un vector vacío para almacenar los valores de TRM_OBSERVADA
TRM_OBSERVADA <- numeric(length(fecha))
# Asignar los valores de TRM_OBSERVADA
for (j in 1:length(fecha)) {
TRM_OBSERVADA[j] <- valores_TRM[j]
}
Cuota_Real_COP=TRM_OBSERVADA*Cuotas_USD
matplot(Cuotas_COP,type = "l", col="#C1FFC1", main="Estimado Cuotas en COP", ylab = "Valor Cuota", xlab = "Cuota")
lines(percentil_5_cuotas, col = "blue", type = "l")
lines(percentil_95_cuotas, col = "red", type = "l")
lines(media_cuotas, col = "black", type = "l")
lines(Cuota_Real_COP, col = "orange", type = "l", lwd = 2)
legend("topright", legend = c( "Percentil 5", "Percentil 95", "Media"),
col = c( "blue", "red", "black"), lty = 1, lwd = c(1, 1, 1, 1))
"Cuota Real COP"## [1] "Cuota Real COP"print(Cuota_Real_COP)## [1] 425373511 447926318 433404610 420112105 440781653"Beneficio sin cobertura"## [1] "Beneficio sin cobertura"Utilidad_POR_USD_Observada=TRM_OBSERVADA-Precio_Entrega
Utilidad_total_observada= Cuotas_USD*Utilidad_POR_USD_ObservadaBeneficio real con cobertura
Valor_Observado_Cuotas_con_cobertura=Cuota_Real_COP-Utilidad_total_observada
matplot(Cuotas_COP_CON_C,type = "l", col="#7FFF00", main="Estimado Cuotas en COP", ylab = "Valor Cuota", xlab = "Cuota")
lines(percentil_5_cuotas_COP_CON_C, type = "l")
lines(percentil_95_cuotas_COP_CON_C, type = "l")
lines(media_cuotas_COP_CON_C, type = "l")
lines(Valor_Observado_Cuotas_con_cobertura, type = "l", lwd=2)
2.5. Cuenta de margen con el flujo de caja operado
# Variables y las fórmulas
Numero_de_contratos <- 1
Nominal_del_contrato <- 1790000*0.7
Precio_inicial <- 4066 # TRM al momento 0
Exposicion_Total = Numero_de_contratos*Nominal_del_contrato*Precio_inicial
Exposicion_Contrato = Exposicion_Total/Numero_de_contratos
Garantia_Inicial <- 0.07
Margen_mantenimiento <- Garantia_Inicial/2
Valor_de_la_garantia_inicial = Exposicion_Total*Garantia_Inicial
Valor_de_la_garantía_minima = Margen_mantenimiento*Valor_de_la_garantia_inicial
Valor_de_la_garantia_inicial*Exposicion_Total## [1] 1816916339784280320Apalancamiento = Exposicion_Total/Valor_de_la_garantia_inicial
Apalancamiento## [1] 14.28571Se liquidan los precios futuros
TRM_Filas <- TRM[c(22, 43, 64, 85, 106), ]
Media_Filas <- rowMeans(TRM_Filas)
Media_TRM <- data.frame(Media_Futuro = Media_Filas)
Tabla_liquidacion <- Media_TRM
Media_TRM$fecha <- fecha
Media_TRM$TRM_OBSERVADA <- TRM_OBSERVADA
Media_TRM <- Media_TRM[, c("fecha", "TRM_OBSERVADA", "Media_Futuro")]
Tabla_liquidacion <- Media_TRM
Dif_Fut_TRM <- diff(Tabla_liquidacion[,3])*-1
Dif_Fut_TRM <- append(0,Dif_Fut_TRM)
Tabla_liquidacion <- cbind(Tabla_liquidacion,(Dif_Fut_TRM*Numero_de_contratos*Nominal_del_contrato))
colnames(Tabla_liquidacion) <- c("Fecha","TRM","Futuro","Liquidacion_Diaria")Se calcula el llamada al margen
margen <- matrix()
tabaux <- matrix()
Llamado_al_margen <- matrix()
for (i in 1:(nrow(Tabla_liquidacion))) {
# Tabla Auxiliar
tabaux[1]=Valor_de_la_garantia_inicial
tabaux[i+1] <- tabaux[i] + Tabla_liquidacion$Liquidacion_Diaria[i+1]
# Llamado al Margen
Llamado_al_margen[i] <- if(tabaux[i]<Valor_de_la_garantía_minima){Valor_de_la_garantia_inicial-tabaux[i]}
else{0}
# Margen
margen[i] <- tabaux[i]+Llamado_al_margen[i]
}
margen <- na.omit(margen)
Tabla_liquidacion <- cbind(Tabla_liquidacion,margen,Llamado_al_margen,Dif_Fut_TRM)
print(Tabla_liquidacion)## Fecha TRM Futuro Liquidacion_Diaria margen Llamado_al_margen
## 1 17/10/2022 4636.83 4443.580 0 356628860 0
## 2 17/11/2022 4922.70 4444.799 -1526874 355101986 0
## 3 17/12/2022 4802.48 4441.568 4048640 359150626 0
## 4 17/01/2023 4693.99 4436.843 5920055 365070680 0
## 5 17/02/2023 4966.33 4435.516 1662065 366732745 0
## Dif_Fut_TRM
## 1 0.000000
## 2 -1.218575
## 3 3.231157
## 4 4.724704
## 5 1.3264692.6 ¿Cuál es la probabilidad de ser llamado al margen si solo se deposita en la cuenta el margen inicial?
llamadas_al_margen <- sum(Llamado_al_margen > 0)
probabilidad_llamado_al_margen <- llamadas_al_margen / nrow(Tabla_liquidacion)
cat("La probabilidad de ser llamado al margen es:", probabilidad_llamado_al_margen)## La probabilidad de ser llamado al margen es: 0La probabilidad de ser llamado al margen si solo se deposita en la cuenta el margen inicial es nula
¿Cuánto debería de haber en la cuenta de margen al inicio para que la probabilidad de ser llamado al margen antes de cubrir el primer flujo sea menor al 1%?
# Definir la probabilidad objetivo
probabilidad_objetivo <- 0.01
# Definir el rango inicial para la búsqueda binaria
min_garantia <- 0
max_garantia <- Exposicion_Total
# Realizar búsqueda binaria para encontrar la garantía inicial adecuada
while (max_garantia - min_garantia > 1) {
# Calcular la garantía inicial candidata
garantia_candidata <- (max_garantia + min_garantia) / 2
# Calcular el valor mínimo de la garantía
valor_de_la_garantia_minima <- Margen_mantenimiento * garantia_candidata
# Calcular la probabilidad de ser llamado al margen
probabilidad_llamado_al_margen <- mean(margen < valor_de_la_garantia_minima)
# Ajustar el rango según la probabilidad calculada
if (probabilidad_llamado_al_margen < probabilidad_objetivo) {
max_garantia <- garantia_candidata
} else {
min_garantia <- garantia_candidata
}
}
# La garantía inicial necesaria será el promedio de los valores min_garantia y max_garantia
garantia_inicial_necesaria <- (max_garantia + min_garantia) / 2
# Imprimir el resultado
cat("La garantía inicial necesaria para que la probabilidad de ser llamado al 1% es:", garantia_inicial_necesaria)## La garantía inicial necesaria para que la probabilidad de ser llamado al 1% es: 0.29655053. Tercera Parte
Modelo Vasicek
dr(t) = k(- r_0)dt + dW
Como resultan las tasas simuladas con 10 iteraciones, para los siguientes 10 periodos, a 252 días.
r0<-0.0387
theta<-0.08
k<-0.44
beta<-0.03
n<-10
T<-10
m<-252
dt<-T/m
r<-matrix(0,m+1,n)
r[1,]<-r0
for (j in 1:n) {
for (i in 2:(m+1)) {
dr<-k*(theta-r[i-1,j])*dt+beta*sqrt(dt)*rnorm(1,0,1)
r[i,j]<-r[i-1,j]+dr
}
}t1<-seq(0,T,dt)
rT.expected <- theta+(r0-theta)*exp(-k*t)
rT.stdev<-sqrt(beta^2/(2*k)*(1-exp(-2*k*t)))
matplot(t1, r[,1:10], type="l", lty=1, main="Short Rate Paths", ylab="rt")
abline(h=theta, col="red", lty=2)
lines(t, rT.expected, lty=2)
lines(t, rT.expected + 2*rT.stdev, lty=2)
lines(t, rT.expected - 2*rT.stdev, lty=2)
points(0,r0)
Con la curva de short rate paths se puede observar la evolución del comportamiento de las tasas de interés a corto plazo, sobre estas se espera un crecimiento constante en la mitad del tiempo y al final un crecimiento mas contundente, en su momento de estabilidad podemos deducir que la economía no tuvo mucha variación ni factores que hicieran que fluctuara mucho en el mercado
Como quedan las curvas yield de ambas tasas en los periodos descritos.
## function to find ZCB price using Vasicek model
VasicekZCBprice <-
function(r0, k, theta, beta, T){
b.vas <- (1/k)*(1-exp(-T*k))
a.vas <- (theta-beta^2/(2*k^2))*(T-b.vas)+(beta^2)/(4*k)*b.vas^2
return(exp(-a.vas-b.vas*r0))
}
## define model parameters for plotting yield curves
theta <- 0.10
k <- 0.5
beta <- 0.03
r0 <- seq(0.00, 0.20, 0.05)
n <- length(r0)
yield <- matrix(0, 10, n)
for(i in 1:n){
for(T in 1:10){
yield[T,i] <- -log(VasicekZCBprice(r0[i], k, theta, beta, T))/T
}
}
maturity <- seq(1, 10, 1)
matplot(maturity, yield, type="l", col="black", lty=1, main="Yield Curve Shapes")
abline(h=theta, col="red",lty=2)
En la grafica de la curva de yield podemos analizar la relacion que se tiene con los rendimientos y la madurez de la TRM, la cual representan el riesgo que se tiene, Presentan un compartimiento constante en el cual se observa que su estado en el mercado no ha sido tan fluctuante en la madurez de 5 a 10
Opciones - Arboles Binomiales - Laboratorio 3
tick = read.table("C:/Users/Felipe/OneDrive - INSTITUTO TECNOLOGICO METROPOLITANO - ITM/Derivados Financieros/Opciones/opciones.txt", header = TRUE)Se realizo el analisis con los activos correspondientes al mercado NasDaq, acorde a unas tendencias del activo desde el 2014 hasta la fecha del 17 de abril del 2024. Las acciones corresponden a:
-EBAY: eBay es un sitio destinado a la subasta y comercio electrónico de productos a través de internet.
-ADBE: Adobe Inc., antes Adobe Systems Incorporated, es una empresa de software estadounidense.
-FTNT: Fortinet es una empresa multinacional de Estados Unidos. Se dedica al desarrollo y la comercialización de software, dispositivos y servicios de ciberseguridad.
Se descargan los paquetes requeridos para el analisis
options(warn = -1)
suppressPackageStartupMessages({
library(tidyquant)
library(plotly)
library(timetk)
library(tidyverse)
library(quantmod)
library(gower)
library(tseries)
library(xts)
library(TTR)
library(ROCR)
library(ROCR)
library(RQuantLib)
library(Deriv)
library(ggplot2)
})Fijar la base de datos
attach(tick)
names(tick)## [1] "Date" "EBAY" "ADBE" "FTNT"options(scipen = 999)
head(tick)## Date EBAY ADBE FTNT
## 1 1/6/2017 31.87507 141.38 7.842
## 2 2/6/2017 32.36065 143.48 7.810
## 3 5/6/2017 32.57138 143.59 7.874
## 4 6/6/2017 32.49809 143.03 7.818
## 5 7/6/2017 32.77294 143.62 7.840
## 6 8/6/2017 33.11194 142.63 7.904Creación del portafolio óptimo de inversión
Optimización del portafolio, utilizando el óptimo de Markowitz
tick <- c('EBAY', 'ADBE', 'FTNT')
price_data <- tq_get(tick, from = '2017-06-01', to = '2024-04-17', get = 'stock.prices')
log_ret_tidy <- price_data %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = 'daily',
col_rename = 'ret',
type = 'log')
head(na.omit(log_ret_tidy))## # A tibble: 6 × 3
## # Groups: symbol [1]
## symbol date ret
## <chr> <date> <dbl>
## 1 EBAY 2017-06-01 0
## 2 EBAY 2017-06-02 0.0151
## 3 EBAY 2017-06-05 0.00649
## 4 EBAY 2017-06-06 -0.00225
## 5 EBAY 2017-06-07 0.00842
## 6 EBAY 2017-06-08 0.0103log_ret_xts <- log_ret_tidy %>%
spread(symbol, value = ret) %>%
tk_xts()## Using column `date` for date_var.#log_ret_xts[is.na(log_ret_xts)] <- 0
head(log_ret_xts)## ADBE EBAY FTNT
## 2017-06-01 0.0000000000 0.000000000 0.000000000
## 2017-06-02 0.0147442876 0.015118960 -0.004088948
## 2017-06-05 0.0007663679 0.006491160 0.008161245
## 2017-06-06 -0.0039076009 -0.002253106 -0.007137455
## 2017-06-07 0.0041164988 0.008422485 0.002810107
## 2017-06-08 -0.0069169899 0.010290871 0.008130082Analisis técnico
Datos y acciones utilizadas
actions<-c('EBAY', 'ADBE', 'FTNT')
getSymbols(actions, from = '2017-06-01', to = '2024-04-17', src="yahoo")## [1] "EBAY" "ADBE" "FTNT"Medias Moviles
for (action in actions) {
# Media movil para 50 días
SMA50<-SMA(Cl(get(action)), n=50)
# Media movil para 200 días
SMA200<-SMA(Cl(get(action)), n=200)
# Calculo de MACD
MACD<-MACD(Cl(get(action)))
# Calculo de Bandas de Bollinger
BBands<-BBands(Cl(get(action)))
}Resumen de Indicadores
cat("Ultimo precio de cierre", as.numeric(Cl(get(action))[nrow(get(action))]), "\n" )## Ultimo precio de cierre 64.48cat("Media movil para 50 días", as.numeric(SMA50[nrow(SMA50)]), "\n")## Media movil para 50 días 68.7618cat("Media movil para 200 días", as.numeric(SMA200[nrow(SMA200)]), "\n")## Media movil para 200 días 63.02745El ultimo precio de cierre es 64.48. Se puede analizar que en la media móvil de 50 dias se destaca una tendencia bajista, en un corto plazo de 50 dias. La cual permite analizar que las fluctuaciones diarias del precio baja, al compararlo con la media móvil a los 200 dias se percibe que se encuentra un poco por encima del promedio, la cual nos permite analizar como será la tendencia en un largo plazo.
cat("MACD:\n")## MACD:print(summary(MACD))## Index macd signal
## Min. :2017-06-01 Min. :-9.9680 Min. :-8.0214
## 1st Qu.:2019-02-20 1st Qu.:-0.8637 1st Qu.:-0.7765
## Median :2020-11-04 Median : 1.2320 Median : 1.1941
## Mean :2020-11-06 Mean : 0.8382 Mean : 0.8414
## 3rd Qu.:2022-07-26 3rd Qu.: 2.5728 3rd Qu.: 2.4530
## Max. :2024-04-16 Max. : 8.7621 Max. : 7.7135
## NA's :25 NA's :33cat("Bandas de Bollinger:\n")## Bandas de Bollinger:print(summary(BBands))## Index dn mavg up
## Min. :2017-06-01 Min. : 6.87 Min. : 7.361 Min. : 7.497
## 1st Qu.:2019-02-20 1st Qu.:14.55 1st Qu.:15.862 1st Qu.:17.038
## Median :2020-11-04 Median :25.12 Median :27.386 Median :29.607
## Mean :2020-11-06 Mean :32.91 Mean :35.834 Mean :38.760
## 3rd Qu.:2022-07-26 3rd Qu.:52.52 3rd Qu.:58.402 3rd Qu.:62.819
## Max. :2024-04-16 Max. :74.61 Max. :77.595 Max. :89.757
## NA's :19 NA's :19 NA's :19
## pctB
## Min. :-0.5461
## 1st Qu.: 0.3504
## Median : 0.6624
## Mean : 0.6021
## 3rd Qu.: 0.8542
## Max. : 1.4448
## NA's :19Con el indicador MACD se analiza que se encuentra por encima de la señal, lo cual puede dar un mensaje de compra en los activos, la media se encuentra muy cercana a la señal lo cual denota que no se tiene una volatilidad muy amplia. Ademas, con el indicador de Bandas de Bollinger se analiza un comportamiento de unos min muy cercanos, lo cual da a enteder que los precios pueden estar muy cercanos.
Retornos
mean_ret <- colMeans(log_ret_xts)
print(round(mean_ret, 5))## ADBE EBAY FTNT
## 0.00070 0.00026 0.00122Los 3 activos generan una rentabilidad, es decir, una ganancia la cual no en una medida muy grande pero eso aporta al portafolio creado por los activos, debido a que se tienen en cuenta que son activos que están teniendo una tendencia bajista en sus comportamientos en el pasar del tiempo
Datos estadisticos
# Covarianza
cov_mat <- cov(log_ret_xts) * 252
print(round(cov_mat,4))## ADBE EBAY FTNT
## ADBE 0.1304 0.0460 0.0861
## EBAY 0.0460 0.0978 0.0448
## FTNT 0.0861 0.0448 0.1754#crear pesos aleatorios
wts <- runif(n = length(tick))
print(wts)## [1] 0.1569330 0.7654246 0.2121442print(sum(wts))## [1] 1.134502#suma de los pesos aleatorios para ser 1
wts <- wts/sum(wts)
print(wts)## [1] 0.1383277 0.6746790 0.1869933sum(wts)## [1] 1# rentabilidad anualizada del portafolio
port_returns <- (sum(wts * mean_ret) + 1)^252 - 1
print(port_returns)## [1] 0.1349176# riesgo del portaflio
port_risk <- sqrt(t(wts) %*% (cov_mat %*% wts))
print(port_risk)## [,1]
## [1,] 0.2783442# asumir rf es 0%
sharpe_ratio <- port_returns/port_risk
print(sharpe_ratio)## [,1]
## [1,] 0.4847147Covarianza: sobre los activos se tiene que sus variaciones son positivas, lo que indica que si un activo aumenta es muy probable que el otro activo tenga similar comportamiento, es decir que aumente, ya que muestra la relación que tienen entre los dos activos que se analizan. Dado que entre mayor sea el valor en positivo mayor es la relación entre ellos.
Rentabilidad anualizada del portafolio: La rentabilidad anualizada del portafolio corresponde a 0.3501, lo cual se puede interpretar como el rendimiento promedio esperado de la cartera de acciones en el portafolio de inversión que permite analizar una visión general del rendimiento a largo durante cierto periodo de tiempo.
Analisis de inversión del Portafolio
Inversión destinada
num_port <- 10000
# matrix de desarrollo
all_wts <- matrix(nrow = num_port,
ncol = length(tick))Analisis de rentabilidad y riesgo del Portafolio
Retornos y datos estadisticos del Portafolio
# Retornos del Portafolio
port_returns <- vector('numeric', length = num_port)
# Desviación del Portafolio
port_risk <- vector('numeric', length = num_port)
# Portfolio Sharpe Ratio
sharpe_ratio <- vector('numeric', length = num_port)
for (i in seq_along(port_returns)) {
wts <- runif(length(tick))
wts <- wts/sum(wts)
all_wts[i,] <- wts
port_ret <- sum(wts * mean_ret)
port_ret <- ((port_ret + 1)^252) - 1
port_returns[i] <- port_ret
port_sd <- sqrt(t(wts) %*% (cov_mat %*% wts))
port_risk[i] <- port_sd
sr <- port_ret/port_sd
sharpe_ratio[i] <- sr
}
portfolio_values <- tibble(Return = port_returns,
Risk = port_risk,
SharpeRatio = sharpe_ratio)
# Convertir la matrix y renombrar las columnas
all_wts <- tk_tbl(all_wts)
colnames(all_wts) <- colnames(log_ret_xts)
# Combinar
portfolio_values <- tk_tbl(cbind(all_wts, portfolio_values))
head(portfolio_values)## # A tibble: 6 × 6
## ADBE EBAY FTNT Return Risk SharpeRatio
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.543 0.384 0.0729 0.155 0.287 0.539
## 2 0.159 0.754 0.0871 0.111 0.282 0.392
## 3 0.268 0.434 0.298 0.183 0.282 0.648
## 4 0.0833 0.552 0.365 0.177 0.286 0.621
## 5 0.638 0.0439 0.318 0.238 0.331 0.717
## 6 0.392 0.251 0.356 0.216 0.299 0.720# Vairaicion minima
min_var <- portfolio_values[which.min(portfolio_values$Risk),]
print(min_var)## # A tibble: 1 × 6
## ADBE EBAY FTNT Return Risk SharpeRatio
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.276 0.571 0.153 0.143 0.275 0.520# El Portafolio con mayor Sharpe Ratio
max_sr <- portfolio_values[which.max(portfolio_values$SharpeRatio),]
print(max_sr)## # A tibble: 1 × 6
## ADBE EBAY FTNT Return Risk SharpeRatio
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.0303 0.0000441 0.970 0.354 0.412 0.857Graficos descriptivos
Variación del Portafolio
var_porta <- min_var %>%
gather(ADBE:FTNT, key = Accion,
value = Peso) %>%
mutate(Asset = as.factor(Accion)) %>%
ggplot(aes(x = fct_reorder(Accion,Peso), y = Peso, fill = Accion)) +
geom_bar(stat = 'identity') +
theme_minimal() +
labs(x = 'Accion', y = 'Peso', title = "Varianza Minima del Portafolio") +
scale_y_continuous(labels = scales::percent)
ggplotly(var_porta)El activo con la minima variazion es FTNT y el mayor es EBAY
Tendencia del Portafolio
tangency_porta <- max_sr %>%
gather(ADBE:FTNT, key = Accion,
value = Peso) %>%
mutate(Accion = as.factor(Accion)) %>%
ggplot(aes(x = fct_reorder(Accion,Peso), y = Peso, fill = Accion)) +
geom_bar(stat = 'identity') +
theme_minimal() +
labs(x = 'Accion', y = 'Peso', title = "Tangencia del Portafolio") +
scale_y_continuous(labels = scales::percent)
ggplotly(tangency_porta)Optimización del Portafolio
opti_porta <- portfolio_values %>%
ggplot(aes(x = Risk, y = Return, color = SharpeRatio)) +
geom_point() +
theme_classic() +
scale_y_continuous(labels = scales::percent) +
scale_x_continuous(labels = scales::percent) +
labs(x = 'Riesgo anuliazado',
y = 'Retornos anualizados',
title = "Optimización del portafolio y frontera eficiente") +
geom_point(aes(x = Risk,
y = Return), data = min_var, color = 'red') +
geom_point(aes(x = Risk,
y = Return), data = max_sr, color = 'red') +
annotate('text', x = 0.35, y = 0.40, label = "Tangencia Portafolio") +
annotate('text', x = 0.35, y = 0.05, label = "Var Min Porta") +
annotate(geom = 'segment', x = 0.30, xend = 0.27, y = 0.05,
yend = 0.1, color = 'red', arrow = arrow(type = "open")) +
annotate(geom = 'segment', x = 0.38, xend = 0.4136, y = 0.40,
yend = 0.365, color = 'red', arrow = arrow(type = "open"))
ggplotly(opti_porta)Creación de Arboles binomiales a través del modelo Cox-Ross-Rubinstein (CRR)
Calculo de Varianzad, Volatilidades y Retornos
# Varianza 1. Precio strike de EBAY y su Volatilidad Implicita
precio_strike <- 50.25
vol_impl <- 3.541# Varianza 2 EBAY
opcion<-c("EBAY")
data_opcion <- lapply(opcion, FUN = function(x){
ROC(Ad(getSymbols(x, from="2023-06-01", to = "2024-04-17", auto.assign = FALSE)),
type = "continuous")
}) #%returns
ret_opcion<-as.data.frame(do.call(merge,data_opcion))
colnames(ret_opcion) <- gsub(".Adjusted", "", colnames(ret_opcion))
ret_opcion<-ret_opcion[-1,]
# Volatilidad de EBAY
var_opcion <-var(ret_opcion)
desve_opcion <- sqrt(var_opcion)
print(desve_opcion)## [1] 0.01717442# Varianza 3
#Volatilidad del portafolio
# Retornos EBAY
opcion_EBAY<-c("EBAY")
data_opcion_EBAY <- lapply(opcion_EBAY, FUN = function(x){
ROC(Ad(getSymbols(x, from="2023-06-01", to = "2024-04-17", auto.assign = FALSE)),
type = "continuous")
}) #%returns
ret_opcion_EBAY<-as.data.frame(do.call(merge,data_opcion_EBAY))
colnames(ret_opcion_EBAY) <- gsub(".Adjusted", "", colnames(ret_opcion_EBAY))
ret_opcion_EBAY<-ret_opcion_EBAY[-1,]
# Retornos ADBE
opcion_ADBE<-c("ADBE")
data_opcion_ADBE <- lapply(opcion_ADBE, FUN = function(x){
ROC(Ad(getSymbols(x, from="2023-06-01", to = "2024-04-17", auto.assign = FALSE)),
type = "continuous")
}) #%returns
ret_opcion_ADBE<-as.data.frame(do.call(merge,data_opcion_ADBE))
colnames(ret_opcion_ADBE) <- gsub(".Adjusted", "", colnames(ret_opcion_ADBE))
ret_opcion_ADBE<-ret_opcion_ADBE[-1,]
# Retornos FTNT
opcion_FTNT<-c("FTNT")
data_opcion_FTNT <- lapply(opcion_FTNT, FUN = function(x){
ROC(Ad(getSymbols(x, from="2023-06-01", to = "2024-04-17", auto.assign = FALSE)),
type = "continuous")
}) #%returns
ret_opcion_FTNTE<-as.data.frame(do.call(merge,data_opcion_FTNT))
colnames(ret_opcion_FTNTE) <- gsub(".Adjusted", "", colnames(ret_opcion_FTNTE))
ret_opcion_FTNTE<-ret_opcion_FTNTE[-1,]
rentabilidad_port<-cbind(ret_opcion_EBAY,ret_opcion_ADBE,ret_opcion_FTNTE)Análisis mediante el Black-Scholes
Datos
opcions <- c('EBAY', 'ADBE', 'FTNT')
start_date <- "2023-06-01"
end_date <- Sys.Date()
getSymbols("EBAY", src = "yahoo", from = "2023-06-01", to = "2024-04-17")## [1] "EBAY"getSymbols("ADBE", src = "yahoo", from = "2023-06-01", to = "2024-04-17")## [1] "ADBE"getSymbols("FTNT", src = "yahoo", from = "2023-06-01", to = "2024-04-17")## [1] "FTNT"tail(EBAY)## EBAY.Open EBAY.High EBAY.Low EBAY.Close EBAY.Volume EBAY.Adjusted
## 2024-04-09 51.80 52.01 51.51 51.96 3566500 51.69703
## 2024-04-10 51.96 52.54 51.90 52.46 4901300 52.19450
## 2024-04-11 52.60 52.65 51.81 51.89 3650900 51.62739
## 2024-04-12 51.71 52.00 51.05 51.31 4246600 51.05033
## 2024-04-15 51.62 51.90 50.74 50.89 3878400 50.63245
## 2024-04-16 50.63 50.75 49.87 50.25 5161500 49.99569tail(ADBE)## ADBE.Open ADBE.High ADBE.Low ADBE.Close ADBE.Volume ADBE.Adjusted
## 2024-04-09 486.00 493.31 483.31 492.55 2548600 492.55
## 2024-04-10 489.39 491.77 480.28 487.22 2487900 487.22
## 2024-04-11 487.36 488.67 479.74 484.28 2978500 484.28
## 2024-04-12 477.95 478.78 468.60 474.09 5620000 474.09
## 2024-04-15 477.02 478.52 468.35 470.10 3353200 470.10
## 2024-04-16 470.00 478.98 468.49 476.22 2660100 476.22tail(FTNT)## FTNT.Open FTNT.High FTNT.Low FTNT.Close FTNT.Volume FTNT.Adjusted
## 2024-04-09 69.14 69.14 67.80 68.22 2799600 68.22
## 2024-04-10 67.08 68.50 67.08 68.13 3641300 68.13
## 2024-04-11 68.61 68.86 67.44 68.22 2917900 68.22
## 2024-04-12 67.47 67.72 65.93 66.45 5132600 66.45
## 2024-04-15 67.08 67.19 64.58 64.73 4911100 64.73
## 2024-04-16 64.62 65.57 64.26 64.48 3015000 64.48Black-Scholes Call Option Price for EBAY
ebay_option_price_quantmod <- function(type, underlying, strike, expire, rate, volatility, div = 0) {
T <- expire
S <- underlying
K <- strike
r <- rate
sigma <- volatility
D <- div
d1 <- (log(S / K) + (r - D + 0.5 * sigma^2) * T) / (sigma * sqrt(T))
d2 <- d1 - sigma * sqrt(T)
if (type == "call") {
option_price <- S * exp(-D * T) * pnorm(d1) - K * exp(-r * T) * pnorm(d2)
} else if (type == "put") {
option_price <- K * exp(-r * T) * pnorm(-d2) - S * exp(-D * T) * pnorm(-d1)
} else {
stop("Invalid option type. Use 'call' or 'put'.")
}
return(option_price)
}Datos obtenidos de los comportamiento de la acción en el mercado de acciones
underlying_price <- 50.25 # Current stock price
strike_price <- 47.5 # Strike price
time_to_expiry <- 3/12
risk_free_rate <- 0.0544 # Risk-free rate (current 3-month bond rate)
dividend_yield <- 1.08 # Dividend yield
volatility <- 0.6104 # Volatility (Blended)
ebay_bs_call_price <- ebay_option_price_quantmod(type = "call",
underlying = underlying_price,
strike = strike_price,
expire = time_to_expiry,
rate = risk_free_rate,
volatility = volatility,
div = dividend_yield)Precio de opción de compra
Opción in-the-money, el precio de ejercicio (47.5) es menor al precio de la acción (50.25)
print(paste("Precio de opción de compra EBAY:", ebay_bs_call_price))## [1] "Precio de opción de compra EBAY: 1.97870515839798"Efecto hipotético de la evolución de los precios ante variaciones de los tipos de interés para un valor determinado
Calcular el precio de la opción Black-Scholes con tipo de interés variable
black_scholes_with_rate_change <- function(S, K, T, r, r_new, sigma, type = "call") {
d1 <- (log(S / K) + ((r_new + (sigma^2) / 2) * T)) / (sigma * sqrt(T))
d2 <- d1 - sigma * sqrt(T)
if (type == "call") {
option_price <- S * pnorm(d1) - K * exp(-r_new * T) * pnorm(d2)
} else {
option_price <- K * exp(-r_new * T) * pnorm(-d2) - S * pnorm(-d1)
}
return(option_price)
}
# Parametros
S <- 50.25 # Current stock price
K <- 47 # Strike price
r <- 0.0544 # Initial risk-free rate
sigma <- 3.541 # Volatility (Blended)
# Definir rango
T <- seq(0, 1, 0.1)
# Calcular los precios de las opciones en diferentes momentos con el tipo de interés inicial
option_prices_initial_rate <- sapply(T, function(t) black_scholes_with_rate_change(S, K, t, r, r, sigma))
# Nuevo tipo de interés (bajada de 25 puntos básicos)
r_new <- r - 0.0025 # Adjusting for 25 basis points drop
# Calculo con el nuevo interes
option_prices_new_rate <- sapply(T, function(t) black_scholes_with_rate_change(S, K, t, r, r_new, sigma))
# Macro de los datos
df_initial_rate <- data.frame(Time = T, OptionPrice = option_prices_initial_rate, RateType = "Initial Rate")
df_new_rate <- data.frame(Time = T, OptionPrice = option_prices_new_rate, RateType = "New Rate")
# Combinar
df_combined <- rbind(df_initial_rate, df_new_rate)Evolución del Precio de la opción con los interes calculados en el tiempo
ggplot(df_combined, aes(x = Time, y = OptionPrice, color = RateType)) +
geom_line() +
labs(title = "Evolución del Precio de la opción con los interes calculados en el tiempo",
x = "Time to Maturity (Years)",
y = "Option Price") +
theme_minimal() +
scale_color_manual(values = c("aquamarine", "red"))
Obtener el precio de la opción de compra ADBE
Función para calcular el precio de la opción Black-Scholes
black_scholes <- function(S, K, T, r, sigma, type = "call") {
d1 <- (log(S / K) + (r + sigma^2 / 2) * T) / (sigma * sqrt(T))
d2 <- d1 - sigma * sqrt(T)
if (type == "call") {
option_price <- S * pnorm(d1) - K * exp(-r * T) * pnorm(d2)
} else {
option_price <- K * exp(-r * T) * pnorm(-d2) - S * pnorm(-d1)
}
return(option_price)
}Datos obtenidos de los comportamiento de la acción en el mercado de acciones
S_adbe <- 476.220001 # Current stock price
K_adbe <- 480 # Strike price
T_adbe <- 0.25 # Time to maturity or expiry (in years)
r_adbe <- 0.0544 # Risk-free rate (current 3-month bond rate)
D_adbe <- 0 # Dividend yield
sigma_adbe <- 0.1836 # Volatility (Blended) Precio de la opción de compra ADBE mediante la fórmula Black-Schole
adbe_bs_price <- black_scholes(S_adbe, K_adbe, T_adbe, r_adbe, sigma_adbe, type = "call")
print(paste("Opción de Compra de ADBE:", adbe_bs_price))## [1] "Opción de Compra de ADBE: 18.7702540654244"La accion ADBE nos indica que presenta una opcion de compra de 18.7702, la cual es un valor en el que el titular tiene derecho a comprar la accion subyacente en el periodo de su validez
Obtener el precio de la opción de compra FTNT
black_scholes <- function(S, K, T, r, sigma, type = "call") {
d1 <- (log(S / K) + (r + sigma^2 / 2) * T) / (sigma * sqrt(T))
d2 <- d1 - sigma * sqrt(T)
if (type == "call") {
option_price <- S * pnorm(d1) - K * exp(-r * T) * pnorm(d2)
} else {
option_price <- K * exp(-r * T) * pnorm(-d2) - S * pnorm(-d1)
}
return(option_price)
}Datos obtenidos de los comportamiento de la acción en el mercado de acciones
S_ftnt <- 64.480003 # Current stock price
K_ftnt <- 60 # Strike price
T_ftnt <- 0.25 # Time to maturity or expiry (in years)
r_ftnt <- 0.0544 # Risk-free rate (current 3-month bond rate)
D_ftnt <- 0 # Dividend yield
sigma_ftnt <- 0.6948 # Volatility (Blended)Precio de la opción de compra FTNT mediante la fórmula Black-Schole
ftnt_bs_price <- black_scholes(S_ftnt, K_ftnt, T_ftnt, r_ftnt, sigma_ftnt, type = "call")
print(paste("Opción de Compra de FTNT:", ftnt_bs_price))## [1] "Opción de Compra de FTNT: 11.4270153583501"Cox Ross Rubinstein Model para EBAY
Modelo de datos
crr_option_price <- function(S0, X, T, r, sigma, n, type = "call") {
delta_t <- T / n
u <- exp(sigma * sqrt(delta_t))
d <- 1 / u
p <- (exp(r * delta_t) - d) / (u - d)
# Generate stock prices at expiration
ST <- S0 * u^(n:0) * d^(0:n)
# Calculate option payoffs at expiration
payoff <- pmax(ST - X, 0) # For a call option
# Backward induction to calculate option price at t=0
for (i in (n - 1):0) {
payoff <- exp(-r * delta_t) * (p * payoff[2:(i + 2)] + (1 - p) * payoff[1:(i + 1)])
}
return(payoff[1])
}
underlying_price <- 50.25 # Current stock price
strike_price <- 47.5 # Strike price
time_to_expiry <- 3/12
risk_free_rate <- 0.0544 # Risk-free rate (current 3-month bond rate)
dividend_yield <- 1.08 # Dividend yield
volatility <- 0.6104 # Volatility (Blended)
n <- 5Precio de la opción de compra EBAY mediante un modelo similar al CRR
ebay_crr_price <- crr_option_price(underlying_price, strike_price, time_to_expiry, risk_free_rate, volatility, n)
cat("Precio de la opción de compra EBAY (tipo CRR):", ebay_crr_price, "\n")## Precio de la opción de compra EBAY (tipo CRR): 10.26548Cox Ross Rubinstein Model para ADBE
underlying_price_adbe <- 476.220001 # Current stock price
strike_price_adbe <- 480 # Strike price
time_to_expiry_adbe <- 0.25 # Time to maturity or expiry (in years)
risk_free_rate_adbe <- 0.0544 # Risk-free rate (current 3-month bond rate)
dividend_yield_adbe <- 0 # Dividend yield
volatility_adbe <- 0.1836 # Volatility (Blended)
n_adbe <- 5Precio de la opción de compra ABDE mediante un modelo similar al CRR
adbe_crr_price <- crr_option_price(underlying_price_adbe, strike_price_adbe,
time_to_expiry_adbe, risk_free_rate_adbe, volatility_adbe, n_adbe)
cat("Precio de la opción de compra ADBE (tipo CRR):", adbe_crr_price, "\n")## Precio de la opción de compra ADBE (tipo CRR): 15.12879El modelo CRR utiliza un enfoque de árbol binomial para valorar opciones, considerando varios factores como el precio actual de la acción, el precio de ejercicio, el tiempo hasta la expiración de la opción, la tasa de interés libre de riesgo y la volatilidad del activo subyacente. De acuerdo con el modelo CRR y las condiciones de mercado proporcionadas, el valor intrínseco de la opción de compra de ADBE es de aproximadamente $15.13. Esto indica que se espera que el precio de la acción de ADBE aumente lo suficiente antes del vencimiento de la opción para que el titular pueda obtener ganancias al ejercer la opción de compra.
Cox Ross Rubinstein Model para FTNT
underlying_price_ftnt <- 64.480003 # Current stock price
strike_price_ftnt <- 60 # Strike price
time_to_expiry_ftnt <- 0.25 # Time to maturity or expiry (in years)
risk_free_rate_ftnt <- 0.0544 # Risk-free rate (current 3-month bond rate)
dividend_yield_ftnt <- 0 # Dividend yield
volatility_ftnt <- 0.6948 # Volatility (Blended)
n_ftnt <- 5Precio de la opción de compra FTNT mediante un modelo similar al CRR
ftnt_crr_price <- crr_option_price(underlying_price_ftnt, strike_price_ftnt,
time_to_expiry_ftnt, risk_free_rate_ftnt, volatility_ftnt, n_ftnt)
cat("Precio de la opción de compra FTNT (tipo CRR):", ftnt_crr_price, "\n")## Precio de la opción de compra FTNT (tipo CRR): 16.10385Opciones Europeas EBAY
s <- 50.25 # Current stock price
k <- 47.5 # Strike price
tt <- 3/12
r <- 0.0544 # Risk-free rate (current 3-month bond rate)
d <- 1.08 # Dividend yield
n <- 0.6104 # Volatility (Blended)
nstep <- 5
# Calcular el precio de la opción call europea de EBAY
european_call_option_price <- EuropeanOption(type = "call", underlying = s,
strike = k, dividendYield = d,
riskFreeRate = r, maturity = tt,
volatility = n)$value
# Calcular el precio de la opción put europea de EBAY
european_put_option_price <- EuropeanOption(type = "put", underlying = s,
strike = k, dividendYield = d,
riskFreeRate = r, maturity = tt,
volatility = n)$value
cat("Precio de opción call europea de EBAY:", european_call_option_price, "\n")## Precio de opción call europea de EBAY: 1.978705cat("Precio de opción put europea de EBAY:", european_put_option_price, "\n")## Precio de opción put europea de EBAY: 10.47726El precio de opción call ebay es de 1.9787, el cual indica que es el precio al cual se tiene derecho para comprar el activo subyacente, se debe de tener en cuenta que un factor importante que influye en el valor del precio es la volatilidad debido a que si esta aumenta también aumentara la volatilidad de la opción call.
El precio de opcion put de ebay es de 10.47726, este es el precio en el que el titular de la opcion tiene derecho de vender la accion subyacente, recordado que como es una opcion europea solo se puede realizar en la fecha de vencimiento lo que en cierta medida puede afectar su precio ya que el tiempo restante influye en la prima de la opcion dejando claro que en cualquiera de los escenarios posibles se cumple cierto riesgo
Modelo de árbol binomial CRR para EBAY
calculate_option_prices <- function(s, k, tt, r, d, n, nstep, crr = TRUE) {
dt <- tt / nstep # Paso de tiempo
u <- exp(n * sqrt(dt)) # Factor de aumento
d <- 1 / u # Factor de reducción
p <- (exp((r - d) * dt) - d) / (u - d) # Probabilidad de subida
# Inicializar una matriz para almacenar los precios de la opción en cada nodo del árbol
option_prices <- matrix(0, nrow = nstep + 1, ncol = nstep + 1)
# Calcular los precios de las opciones en los nodos finales del árbol
for (j in 0:nstep) {
option_prices[nstep + 1, j + 1] <- max(s * u^j * d^(nstep - j) - k, 0)
}
# Calcular los precios de las opciones en los nodos anteriores del árbol
for (i in (nstep - 1):0) {
for (j in 0:i) {
option_prices[i + 1, j + 1] <- exp(-r * dt) * (p * option_prices[i + 2, j + 2] + (1 - p) * option_prices[i + 2, j + 1])
}
}
return(option_prices)
}
# Función para mostrar la matriz del árbol binomial de forma más definida
binomial_tree_ebay <- function(option_prices) {
# Obtener dimensiones de la matriz
nrow <- nrow(option_prices)
ncol <- ncol(option_prices)
# Iterar sobre la matriz y mostrar los precios de la opción
for (i in 1:nrow) {
cat(rep(" ", nrow - i)) # Agregar espacios al principio de cada fila
for (j in 1:ncol) {
if (option_prices[i, j] != 0) { # Solo imprimir valores no nulos
cat(sprintf("%8.2f", option_prices[i, j])) # Imprimir valores de la fila actual
} else {
cat(rep(" ", 1)) # Imprimir espacios en blanco para valores nulos
}
}
cat("\n") # Nueva línea para la siguiente fila
}
}
# Calcular los precios de las opciones en cada nodo del árbol binomial
option_prices <- calculate_option_prices(s, k, tt, r, d, n, nstep)
# Mostrar la matriz del árbol binomial de forma más definida
binomial_tree_ebay(option_prices)## 2.66
## 1.18 5.85
## 0.33 3.00 11.95
## 1.03 7.23 22.11
## 3.22 15.83 35.67
## 10.10 28.18 51.93Opciones Europeas ADBE
s <- 476.220001 # Current stock price
k <- 480 # Strike price
tt <- 3/12
r <- 0.0544 # Risk-free rate (current 3-month bond rate)
d <- 1.08 # Dividend yield
n <- 0.6948 # Volatility (Blended)
nstep <- 5
# Calcular el precio de la opción call europea de ADBE
european_call_option_price_adbe <- EuropeanOption(type = "call", underlying = s,
strike = k, dividendYield = d,
riskFreeRate = r, maturity = tt,
volatility = n)$value
# Calcular el precio de la opción put europea de ADBE
european_put_option_price_adbe <- EuropeanOption(type = "put", underlying = s,
strike = k, dividendYield = d,
riskFreeRate = r, maturity = tt,
volatility = n)$value
cat("Precio de opción call europea de ADBE:", european_call_option_price_adbe, "\n")## Precio de opción call europea de ADBE: 18.39353cat("Precio de opción put europea de ADBE:", european_put_option_price_adbe, "\n")## Precio de opción put europea de ADBE: 128.3731El elevado precio de la opción de venta europea de ADBE indica una expectativa de un posible descenso del precio de la acción, mientras que el precio relativamente bajo de la opción de compra europea indica una menor expectativa de un aumento significativo del precio de la acción. En resumen, los precios de estas opciones reflejan las perspectivas del mercado sobre la evolución futura del precio de la acción de ADBE.
Modelo de árbol binomial CRR para ADBE
calculate_option_prices_adbe <- function(s, k, tt, r, d, n, nstep, crr = TRUE) {
dt <- tt / nstep # Paso de tiempo
u <- exp(n * sqrt(dt)) # Factor de aumento
d <- 1 / u # Factor de reducción
p <- (exp((r - d) * dt) - d) / (u - d) # Probabilidad de subida
# Inicializar una matriz para almacenar los precios de la opción en cada nodo del árbol
option_prices <- matrix(0, nrow = nstep + 1, ncol = nstep + 1)
# Calcular los precios de las opciones en los nodos finales del árbol
for (j in 0:nstep) {
option_prices[nstep + 1, j + 1] <- max(s * u^j * d^(nstep - j) - k, 0)
}
# Calcular los precios de las opciones en los nodos anteriores del árbol
for (i in (nstep - 1):0) {
for (j in 0:i) {
option_prices[i + 1, j + 1] <- exp(-r * dt) * (p * option_prices[i + 2, j + 2] + (1 - p) * option_prices[i + 2, j + 1])
}
}
return(option_prices)
}
# Función para mostrar la matriz del árbol binomial de forma más definida
binomial_tree_adbe <- function(option_prices) {
# Obtener dimensiones de la matriz
nrow <- nrow(option_prices)
ncol <- ncol(option_prices)
# Iterar sobre la matriz y mostrar los precios de la opción
for (i in 1:nrow) {
cat(rep(" ", nrow - i)) # Agregar espacios al principio de cada fila
for (j in 1:ncol) {
if (option_prices[i, j] != 0) { # Solo imprimir valores no nulos
cat(sprintf("%8.2f", option_prices[i, j])) # Imprimir valores de la fila actual
} else {
cat(rep(" ", 1)) # Imprimir espacios en blanco para valores nulos
}
}
cat("\n") # Nueva línea para la siguiente fila
}
}
# Calcular los precios de las opciones en cada nodo del árbol binomial
option_prices <- calculate_option_prices_adbe(s, k, tt, r, d, n, nstep)
# Mostrar la matriz del árbol binomial de forma más definida
binomial_tree_adbe(option_prices)## 26.41
## 11.05 57.08
## 2.85 27.39 116.42
## 8.53 65.00 219.30
## 25.50 143.84 370.70
## 76.26 278.97 555.55Opciones Europeas FTNT
s <- 64.480003 # Current stock price
k <- 60 # Strike price
tt <- 0.25 # Time to maturity or expiry (in years)
r <- 0.0544 # Risk-free rate (current 3-month bond rate)
d <- 0 # Dividend yield
n <- 0.6948 # Volatility (Blended)
nstep <- 5
# Calcular el precio de la opción call europea de FTNT
european_call_option_price_ftnt <- EuropeanOption(type = "call", underlying = s,
strike = k, dividendYield = d,
riskFreeRate = r, maturity = tt,
volatility = n)$value
# Calcular el precio de la opción put europea de FTNT
european_put_option_price_ftnt <- EuropeanOption(type = "put", underlying = s,
strike = k, dividendYield = d,
riskFreeRate = r, maturity = tt,
volatility = n)$value
# Imprimir los resultados
cat("Precio de opción call europea de FTNT:", european_call_option_price_ftnt, "\n")## Precio de opción call europea de FTNT: 11.42702cat("Precio de opción put europea de FTNT:", european_put_option_price_ftnt, "\n")## Precio de opción put europea de FTNT: 6.136536El precio de una opción call europea tiende a aumentar cuando el precio del activo subyacente aumenta, mientras que el precio de una opción put europea tiende a aumentar cuando el precio del activo subyacente disminuye. Además, ambos precios son influenciados por factores como el tiempo hasta la expiración, la tasa de interés y la volatilidad del activo subyacente. En el caso del activo, el precio de la opción call europea de FTNT es de 11.42702, lo que sugiere una expectativa de un aumento en el precio de FTNT, mientras que el precio de la opción put europea de FTNT es de 6.136536, indicando una expectativa de una posible disminución en el precio de FTNT.
Modelo de árbol binomial CRR para FTNT
calculate_option_prices_ftnt <- function(s, k, tt, r, d, n, nstep, crr = TRUE) {
dt <- tt / nstep # Paso de tiempo
u <- exp(n * sqrt(dt)) # Factor de aumento
d <- 1 / u # Factor de reducción
p <- (exp((r - d) * dt) - d) / (u - d) # Probabilidad de subida
# Inicializar una matriz para almacenar los precios de la opción en cada nodo del árbol
option_prices <- matrix(0, nrow = nstep + 1, ncol = nstep + 1)
# Calcular los precios de las opciones en los nodos finales del árbol
for (j in 0:nstep) {
option_prices[nstep + 1, j + 1] <- max(s * u^j * d^(nstep - j) - k, 0)
}
# Calcular los precios de las opciones en los nodos anteriores del árbol
for (i in (nstep - 1):0) {
for (j in 0:i) {
option_prices[i + 1, j + 1] <- exp(-r * dt) * (p * option_prices[i + 2, j + 2] + (1 - p) * option_prices[i + 2, j + 1])
}
}
return(option_prices)
}
# Función para mostrar la matriz del árbol binomial de forma más definida
binomial_tree_ftnt <- function(option_prices) {
# Obtener dimensiones de la matriz
nrow <- nrow(option_prices)
ncol <- ncol(option_prices)
# Iterar sobre la matriz y mostrar los precios de la opción
for (i in 1:nrow) {
cat(rep(" ", nrow - i)) # Agregar espacios al principio de cada fila
for (j in 1:ncol) {
if (option_prices[i, j] != 0) { # Solo imprimir valores no nulos
cat(sprintf("%8.2f", option_prices[i, j])) # Imprimir valores de la fila actual
} else {
cat(rep(" ", 1)) # Imprimir espacios en blanco para valores nulos
}
}
cat("\n") # Nueva línea para la siguiente fila
}
}
# Calcular los precios de las opciones en cada nodo del árbol binomial
option_prices <- calculate_option_prices_ftnt(s, k, tt, r, d, n, nstep)
# Mostrar la matriz del árbol binomial de forma más definida
binomial_tree_ftnt(option_prices)## 4.62
## 2.05 9.76
## 0.57 5.00 19.26
## 1.71 11.57 34.66
## 5.12 24.45 55.17
## 15.32 42.76 80.21Creación de coberturas
# Long Straddle payoff Ebay
prices <- seq(40,55,1) # Vector of prices
strike <- 47 # strike price for both put and call
premium_call <- 1.978705 # option price call
premium_put <- 10.47726 # option price put
# call option payoff at expiration
intrinsicValuesCall <- prices - strike - premium_call
payoffLongCall <- pmax(-premium_call,intrinsicValuesCall)
# put option payoff at expiration
intrinsicValuesPut <- strike - prices - premium_put
payoffLongPut <- pmax(-premium_put,intrinsicValuesPut)
# The payoff of the Strategy is the sum of the call and put payoff. Need
# to sum wise element by element between the two vectors
payoff <- rowSums(cbind(payoffLongCall,payoffLongPut))
# Make a DataFrame with all the variable to plot it with ggplot
results <- data.frame(cbind(prices,payoffLongCall,payoffLongPut,payoff))
ggplot(results, aes(x=prices)) +
geom_line(aes(y = payoffLongCall, color = "LongCall")) +
geom_line(aes(y = payoffLongPut, color="LongPut"))+
geom_line(aes(y=payoff, color = 'Payoff')) +
scale_colour_manual("",
breaks = c("LongCall", "LongPut", "Payoff"),
values = c("red", "blue", "black")) + ylab("Payoff")+
ggtitle("Long Straddle Payoff")
Cobertura simulada del activo FTNT
s <- 64.480003 # Current stock price
k <- 60 # Strike price
tt <- 0.25 # Time to maturity or expiry (in years)
r <- 0.0544 # Risk-free rate (current 3-month bond rate)
d <- 0 # Dividend yield
n <- 0.6948 # Volatility (Blended)
nstep <- 5
# Valor de las opciones de compra (call) y venta (put)
d1 <- (log(s/k) + (r + 0.5 * n^2) * tt) / (n * sqrt(tt))
d2 <- d1 - n * sqrt(tt)
call_price <- s * pnorm(d1) - k * exp(-r * tt) * pnorm(d2)
put_price <- k * exp(-r * tt) * pnorm(-d2) - s * pnorm(-d1)
# Payoff de la estrategia Long Straddle
prices <- seq(50,70,1) # Vector of prices
strike <- 60 # strike price for both put and call
premium_call <- 11.42702 # option price call
premium_put <- 6.136536 # option price put
# Payoff de la opci??n de compra (call) al vencimiento
intrinsicValuesCall <- prices - k - premium_call
payoffLongCall <- pmax(-premium_call, intrinsicValuesCall)
# Payoff de la opci??n de venta (put) al vencimiento
intrinsicValuesPut <- k - prices - premium_put
payoffLongPut <- pmax(-premium_put, intrinsicValuesPut)
# Payoff de la estrategia Long Straddle
payoff <- payoffLongCall + payoffLongPut
# Crear un DataFrame con los resultados para graficar
results <- data.frame(prices, payoffLongCall, payoffLongPut, payoff)
# Graficar el payoff de la estrategia Long Straddle
library(ggplot2)
ggplot(results, aes(x = prices)) +
geom_line(aes(y = payoffLongCall, color = "LongCall")) +
geom_line(aes(y = payoffLongPut, color = "LongPut")) +
geom_line(aes(y = payoff, color = "Straddle Payoff")) +
scale_color_manual("",
breaks = c("LongCall", "LongPut", "Straddle Payoff"),
values = c("red", "blue", "black")) +
ylab("Payoff") +
ggtitle("Long Straddle Payoff")
BSM and Swaps - Laboratorio 4
bsm = read.table("C:/Users/Felipe/OneDrive - INSTITUTO TECNOLOGICO METROPOLITANO - ITM/Derivados Financieros/BSM and Swaps/BSM (1).txt", header = TRUE)
# Definimos medidas
prome_nflx <- mean(bsm$NFLX)
prome_ebay <- mean(bsm$EBAY)
ret_nflx <- diff(log(bsm$NFLX))
ret_ebay <- diff(log(bsm$EBAY))El promedio de las acciones de NFLX es de 420.036 y de EBAY es de 47.103 lo cual indica que en cierto momento presentaron una tendencia alcista donde sus precios fueron creciendo
#Definimos formulas de uso
Black Scholes Merton y valoracion de las griegas
black_scholes_merton <- function(So, K, r, VencimientoDias, sigma, Stcall, Stput) {
Ano <- 252
#Definir los vencimientos a partir de un número de días establecido
VencimientoDias = seq(from = VencimientoDias, by = 90, length.out = 6)
#Definir un conjunto de Volatilidad a partir de un valor sigma inicial
sigma = seq(from = sigma, by = 0.05, length.out = 6)
## Cálculo del vencimiento
T <- VencimientoDias / Ano
#Definir d1 y d2
d1 <- (log(So/K) + (r + ((sigma^2)/2)) * T) / (sigma * sqrt(T))
d2 <- (log(So/K) + (r - ((sigma^2)/2)) * T) / (sigma * sqrt(T))
# Definir N1 y N2 para la posición Call y Put
Nd1 <- pnorm(d1)
Nd2 <- pnorm(d2)
Nd1P <- pnorm(-d1)
Nd2P <- pnorm(-d2)
#Valoración Call
Call <- So * Nd1 - (K * exp(-r * T) * Nd2)
#Valoración Put
Put <- (K * exp(-r * T) * Nd2P) - So * Nd1P
##Crear vector de varios precios st a partir de un stc dado
St <- seq(from = Stcall - 30 * 5, to = Stcall + 30 * 5, by = 5)
num_filas <- length(St)
num_columnas <- length(sigma)
## Matriz resultados de la Valoración Call
resultadosCall <- matrix(NA, nrow = num_filas, ncol = num_columnas)
##
for (i in 1:num_filas) {
for (j in 1:num_columnas) {
resultado <- (St[i] * pnorm((log(St[i]/K) + (r + ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j]))) -
K * exp(-r * T[j]) * pnorm((log(St[i]/K) + (r - ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j])))) /
Call[j]
resultadosCall[i, j] <- resultado
}
}
#Definir el nombre de las columnas
colnames(resultadosCall) <- paste("Vto a", VencimientoDias, "días")
##Crear vector de varios precios st a partir de un stp dado
StP <- seq(from = Stput - 30 * 5, to = Stcall + 30 * 5, by = 5)
#matriz de resultados de la valoración Put
resultadosPut <- matrix(NA, nrow = num_filas, ncol = num_columnas)
for (i in 1:num_filas) {
for (j in 1:num_columnas) {
resultado <- (K * exp(-r * T[j]) * pnorm(-(log(StP[i]/K) + (r - ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j])))
- StP[i] * pnorm(-(log(StP[i]/K) + (r + ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j])))) /
Put[j]
resultadosPut[i, j] <- resultado
}
}
colnames(resultadosPut) <- paste("Vto a", VencimientoDias, "días")
#incluir columna de los valores de St para la posición Call en la matriz de resultados
CallTable <- cbind(St, resultadosCall)
# definir la tabla como un dataframe para evitar error en el tipo de datos
CallTable <- as.data.frame(CallTable)
#Proceso similar al anterior realizado ahora para la posición Put
PutTable <- cbind(StP, resultadosPut)
PutTable <- as.data.frame(PutTable)
# Graficar Call
colores <- rainbow(num_columnas)
matplot(1:num_filas, resultadosCall, type = "l", col = colores, lty = 1, xlab = "Índice", ylab = "Valor", main = "Gráfico de Líneas de Resultados Call")
legend("topleft", legend = colnames(resultadosCall), col = colores, lty = 1, cex = 0.4)
grid()
png(filename = "CallPlot.png")
dev.off()
# Graficar Put
colores <- rainbow(num_columnas)
matplot(1:num_filas, resultadosPut, type = "l", col = colores, lty = 1, xlab = "Índice", ylab = "Valor", main = "Gráfico de Líneas de Resultados Put")
legend("topright", legend = colnames(resultadosPut), col = colores, lty = 1, cex = 0.4)
grid()
png(filename = "PutPlot.png")
dev.off()
return(list(CallTable = CallTable, PutTable = PutTable))
}
# Valoracion de griegas
valoracion_griegas <- function(t=0,T,S,K,r,q=0,sigma,isPut=0) {
# t and T are measured in years; all parameters are annualized
# q is the continuous dividend yield
d1 <- (log(S/K)+(r-q+sigma^2/2)*(T-t))/(sigma*sqrt(T-t))
d2 <- d1-sigma*sqrt(T-t)
binary <- pnorm(-d2)*exp(-r*T)
# Call Delta at t
Delta <- exp(-q*(T-t))*pnorm(d1)
Gamma <- exp(-q*(T-t))*exp(-d1^2/2)/sqrt(2*pi)/S/sigma/sqrt(T-t)
Vega <- S*exp(-q*(T-t))/sqrt(2*pi)*exp(-d1^2/2)*sqrt(T-t)
Theta <- -S*exp(-q*(T-t))*sigma/sqrt(T-t)/2*dnorm(d1) - r*K*exp(-r*(T-t))*pnorm(d2) +
q*S*exp(-q*(T-t))*pnorm(d1)
Rho <- (T-t)*K*exp(-r*(T-t))*pnorm(d2)
# Black-Scholes formula for Calls
BSprice <- -K*exp(-r*(T-t))*pnorm(d2)+S*Delta
if (isPut==1) {
Delta <- -exp(-q*(T-t))*pnorm(-d1)
BSprice <- S*Delta+K*exp(-r*(T-t))*pnorm(-d2)
Theta <- -S*exp(-q*(T-t))*sigma/sqrt(T-t)/2*dnorm(d1) + r*K*exp(-r*(T-t))*pnorm(-d2) -
q*S*exp(-q*(T-t))*pnorm(-d1)
Rho <- -(T-t)*K*exp(-r*(T-t))*pnorm(-d2)
}
Bank <- BSprice-Delta*S
return (list(Delta=Delta,Gamma=Gamma,Theta=Theta,Vega=Vega,Rho=Rho,Price=BSprice,d1=d1,d2=d2,B=Bank))
}Valore los precios de las opciones mediante el modelo de Black, Scholes y Merton. Calcule y analice las griegas
Netflix
# Simulacion 1 So = 355.06, K = 420, StCall= 360 y StPut = 420
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 355.06, K = 420, r = 0.05160, VencimientoDias = 90, sigma = sd(ret_nflx), Stcall = 360, Stput = 420)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=360,K=420,r=0.05160,q=0,sigma=sd(ret_nflx),isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=420,K=420,r=0.05160,q=0,sigma=sd(ret_nflx),isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta Gamma
## 1 0.0000000000000000000000199256 0.00000000000000000000003858025
## 2 -0.2013223207740032494328374923 0.04663134252354541459117953650
## Theta Vega
## 1 -0.00000000000000000000260083 0.0000000000000000000344706
## 2 0.72761768781622437884948340 56.7094394188440702464504284
## Rho Price d1
## 1 0.000000000000000000001653008 0.00000000000000000000001017769 -9.9043604
## 2 -19.670454382522756020534870913 0.68326093251722852528473595157 0.8369074
## d2 B type
## 1 -9.9187116 -0.000000000000000000007163037 Call
## 2 0.8225561 85.238635657598592842987272888 PutEn un vencimiento de 90 días para un call , tenemos un delta de 1.992560e-23 lo que significa cuanto cambia el precio de la opción en comparación con los cambios del precio subyacente, por lo tanto, un aumento en el precio del subyacente, el precio de la opción call aumentara en 1.992560e-23.
Se tiene un gamma de 3.858025e-23 el cual indica el cambio de la tasa de cambio de delta en relación con los cambios del precio subyacente y así mismo poder evaluar el riesgo de volatilidad de la cartera de las opciones .El vega de 3.447060e-20 indica que si hay un aumento del 1%, por lo tanto el precio de la opción call aumentara en 3.447060e-20 Con un vencimiento de 90 dias para un put, se tiene un theta de 7.276177e-01 lo que indica que en el momento que se mantiene todo constante, el valor de la opción en put aumentara en 7.276177e-01 unidades por dia. Adicionalmente, se tiene un Rho de -1.967045e+01 lo que al ser negativo indica que disminuye su valor cuando hay un aumento en la tasa de interés
# Simulacion 2 So = 355.06, K = 420, StCall= 420 y StPut = 490
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 355.06, K = 420, r = 0.05160, VencimientoDias = 90, sigma = sd(ret_nflx), Stcall = 420, Stput = 490)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=420,K=420,r=0.05160,q=0,sigma=sd(ret_nflx),isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=490,K=420,r=0.05160,q=0,sigma=sd(ret_nflx),isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta
## 1 0.798677679225996750567162507650209591
## 2 -0.000000000000000000000000000000265829
## Gamma
## 1 0.0466313425235454145911795365009311354
## 2 0.0000000000000000000000000000004408977
## Theta Vega
## 1 -20.68784919442044056836493837181478739 56.7094394188440702464504283852875233
## 2 -0.00000000000000000000000000004050969 0.0000000000000000000000000007298084
## Rho
## 1 76.10533668293639664170768810436129570
## 2 -0.00000000000000000000000000003009589
## Price d1 d2
## 1 5.6548329821942502348974812775850296021 0.8369074 0.8225561
## 2 0.0000000000000000000000000000001593235 11.5781751 11.5638238
## B type
## 1 -329.7897922927243712365452665835618973 Call
## 2 0.0000000000000000000000000001304155 Put# Simulacion 3 So = 355.06, K = 420, StCall= 605.5 y StPut = 420
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 355.06, K = 420, r = 0.05160, VencimientoDias = 90, sigma = sd(ret_nflx), Stcall = 605.5, Stput = 420)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=605.5,K=420,r=0.05160,q=0,sigma=sd(ret_nflx),isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=420,K=420,r=0.05160,q=0,sigma=sd(ret_nflx),isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta
## 1 1.0000000
## 2 -0.2013223
## Gamma
## 1 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001467977
## 2 0.04663134252354541459117953650093113537877798080444335937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## Theta
## 1 -21.4154669
## 2 0.7276177
## Vega
## 1 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000371045
## 2 56.7094394188440702464504283852875232696533203125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## Rho Price d1 d2 B type
## 1 95.77579 190.4715720 26.3259558 26.3116045 -415.02843 Call
## 2 -19.67045 0.6832609 0.8369074 0.8225561 85.23864 PutEn la valoracion de 90 dias con un st call de 605.5 y un st put de 420 tenemos un gamma en call de 1.467977e-25 lo que significa que si el precio del subyacente aumenta en 1 unidad, el delta de la opción aumentara en aproximadamente 1.467977e-25, se tiene un theta de -21.4154669 lo que da a entender es que el valor de la opción disminuirá en aproximadamente -21.41 a medida que pasa el tiempo siendo lo otro todo igual.Un rho de 95.77579 indica que el valor de la opción aumenta en 95.77579 si las tasas de intereses suben
Ebay
# Simulacion 1 So = 33.30934, K = 45, StCall= 48.5 y StPut = 44.5
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 33.309, K = 45, r = 0.05160, VencimientoDias = 90, sigma = sd(ret_ebay), Stcall = 48.5, Stput = 44.5)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=48.5,K=45,r=0.05160,q=0,sigma=sd(ret_ebay),isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=44.5,K=45,r=0.05160,q=0,sigma=sd(ret_ebay),isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta Gamma Theta Vega
## 1 1.0000000 0.00000000000000002079826 -2.2945143 0.0000000000000002334716
## 2 -0.4685591 0.89963004359628584438724 0.7032542 8.5017337510823836055351
## Rho Price d1 d2 B type
## 1 10.261692 4.0326684 8.74333208 8.7333978 -44.46733 Call
## 2 -4.848767 0.1604437 0.07889244 0.0689582 21.01132 Put# Simulacion 2 So = 33.30934, K = 45, StCall= 42 y StPut = 63
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 33.309, K = 45, r = 0.05160, VencimientoDias = 90, sigma = sd(ret_ebay), Stcall = 42, Stput = 63)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=42,K=45,r=0.05160,q=0,sigma=sd(ret_ebay),isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=63,K=45,r=0.05160,q=0,sigma=sd(ret_ebay),isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta
## 1 0.000000004696529377534608700513890644501202586980070918798446655273437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 -0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000008523936
## Gamma
## 1 0.0000000664823442418244817293804249658251137589104473590850830078125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004780765
## Theta
## 1 -0.000000035238124624976087588372475334352884601685218513011932373046875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 -0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000378015
## Vega
## 1 0.000000559665367318659257760485314925347211101325228810310363769531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009055283
## Rho
## 1 0.00000004544574477401222861727703161704994272440671920776367187500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 -0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012396
## Price
## 1 0.0000000003226731690672739750460826235745059875625884160399436950683593750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001518987
## d1 d2
## 1 -5.741339 -5.751274
## 2 35.073577 35.063643
## B
## 1 -0.0000001969315606873862931243401863667941142921335995197296142578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000005371598
## type
## 1 Call
## 2 Put# Simulacion 3 So = 33.30934, K = 45, StCall= 53 y StPut = 43
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 33.309, K = 45, r = 0.05160, VencimientoDias = 90, sigma = sd(ret_ebay), Stcall = 53, Stput = 43)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=53,K=45,r=0.05160,q=0,sigma=sd(ret_ebay),isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=43,K=45,r=0.05160,q=0,sigma=sd(ret_ebay),isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta
## 1 1.0000000
## 2 -0.9996278
## Gamma
## 1 0.00000000000000000000000000000000000000000000000000000000000000000001102578
## 2 0.00316384294930163907644260490314991329796612262725830078125000000000000000
## Theta
## 1 -2.294514
## 2 2.292440
## Vega
## 1 0.0000000000000000000000000000000000000000000000000000000000000000001478034
## 2 0.0279174248705441885309852523278095759451389312744140625000000000000000000
## Rho Price d1 d2 B type
## 1 10.26169 8.532668 17.674879 17.664945 -44.46733 Call
## 2 -10.25801 1.467373 -3.372713 -3.382647 44.45137 PutEn conclusion de la opcion Ebay trabajada en las simulaciones anteriores, se denota:
En la opción Ebay con un st call de 48.5 y un st put de 44.5 se tienen los siguientes valores: Theta de -2.2945143 en call, lo que significa que al mantener todo lo demás constante, el valor de la opción disminuirá en 2.294 unidades por dia.un rho de 10.261692 lo que significa que si la tasa de interés aumenta en 1,el precio de la opción en call aumentara en aproximadamente en 10.2616 unidades. Un gamma en put de 8.996300e-01 lo que indica que si el precio del subyacente aumenta, entonces el delta de la opción put. Se tiene un theta de 0.7032542 significa que con todas las demás variables constantes, el valor de la opción aumentara en aproximadamente 0.7032 uniddes por dia
Con un st call de 53 y un st put de 43 se tiene un delta put de -0.9996278 lo que significa que si el precio del activo subyacente disminuye, el precio del valor de la opción aumentara en aprox 0.9996, un rho de call de 10.26169 lo que significa que el valor de la opción aumentara en aproximadamente 10.2616 cuando las tasas de interés aumenten
Valore los precios de las opciones mediante el modelo de Black, Scholes y Merton, pero modificando la tasa de variación implícita. Calcule y analice las griegas
Netflix
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 355.06, K = 420, r = 0.05160, VencimientoDias = 90, sigma = 2.9219, Stcall = 360, Stput = 420)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=360,K=420,r=0.05160,q=0,sigma=2.9219,isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=420,K=420,r=0.05160,q=0,sigma=2.9219,isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta Gamma Theta Vega Rho Price d1
## 1 0.7259064 0.0006592581 -369.2388 57.61078 20.20315 173.7793 0.6004787
## 2 -0.2387587 0.0005258352 -379.7688 62.54484 -72.40172 213.4621 0.7103011
## d2 B type
## 1 -0.8031567 -87.54697 Call
## 2 -0.6933342 313.74077 PutAl modificar la variación implícita, se presenta las siguientes variaciones: Delta en call de 0.7259064 lo que se entiende que si el precio del subyacente aumenta entonces el valor de la opción también aumenta en aproximadamente 0.7259; un gamma en put de 0.0005258352 o que significa que el valor de gamma va aumentando a medida que el precio del subyacente se vaya alejando del precio strike.Con un theta en call de -369.2388 lo que significa que el vaor de la opción va disminuyendo a medida que todo se mantiene constante. Un vega en put de 62.54484 indica que el valor de la opción aumenta cuando la volatilidad implícita del precio subyacente aumente
Ebay
# Llamada a la función con valores específicos y gráficas
resultado <- black_scholes_merton(So = 33.309, K = 45, r = 0.05160, VencimientoDias = 90, sigma = 2.0234, Stcall = 48.5, Stput = 44.5)
#Vencimiento tres meses (12 semanas)
#Call
call_result <- valoracion_griegas(t=0,T=12/52,S=48.5,K=45,r=0.05160,q=0,sigma=2.0234,isPut=0)
#Put
put_result <- valoracion_griegas(t=0,T=12/52,S=44.5,K=45,r=0.05160,q=0,sigma=2.0234,isPut=1)
call_df <- as.data.frame(call_result)
put_df <- as.data.frame(put_result)
call_df$type <- 'Call'
put_df$type <- 'Put'
result_df <- rbind(call_df, put_df)
print(result_df)## Delta Gamma Theta Vega Rho Price d1
## 1 0.7174604 0.007171747 -35.32704 7.877131 3.548449 19.42022 0.5753137
## 2 -0.3132140 0.008192744 -31.63646 7.575461 -7.042089 16.57769 0.4867605
## d2 B type
## 1 -0.3966962 -15.37661 Call
## 2 -0.4852494 30.51572 PutValore los precios de las opciones mediante el modelo de Black, Scholes y Merton, pero modificando la tasa de interés (una con intervalo de crecimiento y decrecimiento de 2%, hasta llegar a un total de 10 puntos de distancia, otra con una simulación de Vasicek de la tasa de interés)
Netflix
black_scholes_merton <- function(So, K, r_range, VencimientoDias, sigma, Stcall, Stput) {
Ano <- 252
# Definir los vencimientos a partir de un número de días establecido
VencimientoDias <- seq(from = VencimientoDias, by = 90, length.out = 6)
# Repetir sigma para cada vencimiento
sigma <- rep(sigma, length(VencimientoDias))
# Cálculo del vencimiento
T <- VencimientoDias / Ano
# Inicializar listas para almacenar resultados
resultados_call <- list()
resultados_put <- list()
griegas_call <- list()
griegas_put <- list()
for (r in r_range) {
# Definir d1 y d2
d1 <- (log(So/K) + (r + ((sigma^2)/2)) * T) / (sigma * sqrt(T))
d2 <- d1 - sigma * sqrt(T)
# Definir N1 y N2 para la posición Call y Put
Nd1 <- pnorm(d1)
Nd2 <- pnorm(d2)
Nd1P <- pnorm(-d1)
Nd2P <- pnorm(-d2)
# Valoración Call
Call <- So * Nd1 - (K * exp(-r * T) * Nd2)
# Valoración Put
Put <- (K * exp(-r * T) * Nd2P) - So * Nd1P
# Calcular las griegas para Call
DeltaCall <- Nd1
GammaCall <- dnorm(d1) / (So * sigma * sqrt(T))
ThetaCall <- (-So * dnorm(d1) * sigma / (2 * sqrt(T)) - r * K * exp(-r * T) * Nd2) / Ano
VegaCall <- So * dnorm(d1) * sqrt(T)
RhoCall <- K * T * exp(-r * T) * Nd2
# Calcular las griegas para Put
DeltaPut <- Nd1 - 1
GammaPut <- dnorm(d1) / (So * sigma * sqrt(T))
ThetaPut <- (-So * dnorm(d1) * sigma / (2 * sqrt(T)) + r * K * exp(-r * T) * Nd2P) / Ano
VegaPut <- So * dnorm(d1) * sqrt(T)
RhoPut <- -K * T * exp(-r * T) * Nd2P
# Almacenar resultados
resultados_call[[paste0("r_", r)]] <- Call
resultados_put[[paste0("r_", r)]] <- Put
griegas_call[[paste0("r_", r)]] <- data.frame(VencimientoDias = VencimientoDias, Delta = DeltaCall, Gamma = GammaCall, Theta = ThetaCall, Vega = VegaCall, Rho = RhoCall)
griegas_put[[paste0("r_", r)]] <- data.frame(VencimientoDias = VencimientoDias, Delta = DeltaPut, Gamma = GammaPut, Theta = ThetaPut, Vega = VegaPut, Rho = RhoPut)
}
return(list(Call = resultados_call, Put = resultados_put, GriegasCall = griegas_call, GriegasPut = griegas_put))
}
# Definir los parámetros
So <- 355.06
K <- 420
sigma <- sd(ret_nflx)
Stcall <- 360
Stput <- 420
VencimientoDias <- 90
# Definir el rango de tasas de interés
tasa <- 0.05160
tasa_mod <- seq(tasa - 0.10, tasa + 0.10, by = 0.02)
# Llamar a la función modificada
resultado_inter <- black_scholes_merton(So, K, tasa_mod, VencimientoDias, sigma, Stcall, Stput)
# Imprimir los resultados para cada tasa de interés
for (r in tasa_mod) {
cat("\nResultados para r =", r, "\n")
print(resultado_inter$Call[[paste0("r_", r)]])
print(resultado_inter$Put[[paste0("r_", r)]])
cat("\nGriegas para Call con r =", r, "\n")
print(resultado_inter$GriegasCall[[paste0("r_", r)]])
cat("\nGriegas para Put con r =", r, "\n")
print(resultado_inter$GriegasPut[[paste0("r_", r)]])
}##
## Resultados para r = -0.0484
## [1] 0.0000000000000000000000001045577 0.0000000000000006256005385786427
## [3] 0.0000000000009726011925181384366 0.0000000000322239814417754617251
## [5] 0.0000000002246116286040898429041 0.0000000007120840855961868956503
## [1] 72.26311 79.71391 87.29461 95.00750 102.85487 110.83906
##
## Griegas para Call con r = -0.0484
## VencimientoDias Delta
## 1 90 0.0000000000000000000000001743933
## 2 180 0.0000000000000005773428170226192
## 3 270 0.0000000000006547015096518772935
## 4 360 0.0000000000176437814445653912642
## 5 450 0.0000000001059519086173374114454
## 6 540 0.0000000002996885479279694125890
## Gamma Theta
## 1 0.0000000000000000000000002878244 -0.00000000000000000000000005238185
## 2 0.0000000000000005236104393567673 -0.00000000000000007764036418372449
## 3 0.0000000000004310698619470260460 -0.00000000000005177271261672428095
## 4 0.0000000000094180421411293512119 -0.00000000000090548542890985475214
## 5 0.0000000000486079043613979811574 -0.00000000000366914831930243468265
## 6 0.0000000001224551397489777698020 -0.00000000000703685035750261867957
## Vega Rho
## 1 0.0000000000000000000003871454 0.00000000000000000000002207697
## 2 0.0000000000014085903552011765 0.00000000000014597552862390893
## 3 0.0000000017394635524333800769 0.00000000024802041088336866932
## 4 0.0000000506718824825950703685 0.00000000890339579752230371457
## 5 0.0000003269063225425620368425 0.00000006677620186619238559084
## 6 0.0000009882678943936894043823 0.00000022648999658937565989357
##
## Griegas para Put con r = -0.0484
## VencimientoDias Delta Gamma Theta
## 1 90 -1 0.0000000000000000000000002878244 -0.08207317
## 2 180 -1 0.0000000000000005236104393567673 -0.08350419
## 3 270 -1 0.0000000000004310698619470260460 -0.08496017
## 4 360 -1 0.0000000000094180421411293512119 -0.08644154
## 5 450 -1 0.0000000000486079043613979811574 -0.08794873
## 6 540 -1 0.0000000001224551397489777698020 -0.08948220
## Vega Rho
## 1 0.0000000000000000000003871454 -152.6154
## 2 0.0000000000014085903552011765 -310.5528
## 3 0.0000000017394635524333800769 -473.9514
## 4 0.0000000506718824825950703685 -642.9536
## 5 0.0000003269063225425620368425 -817.7051
## 6 0.0000009882678943936894043823 -998.3551
##
## Resultados para r = -0.0284
## [1] 0.000000000000000000000006594814 0.000000000000056951366513194427
## [3] 0.000000000126579050270478856235 0.000000005952515447854735860123
## [5] 0.000000058559842381632784373557 0.000000260840530818382443541126
## [1] 69.22168 73.54700 77.91643 82.33039 86.78935 91.29377
##
## Griegas para Call con r = -0.0284
## VencimientoDias Delta
## 1 90 0.00000000000000000000001059077
## 2 180 0.00000000000004906877365913140
## 3 270 0.00000000007751186292178445910
## 4 360 0.00000000289940061612906398864
## 5 450 0.00000002409760396127958746292
## 6 540 0.00000009411773666983289169698
## Gamma Theta
## 1 0.00000000000000000000001681705 -0.00000000000000000000000333122
## 2 0.00000000000004145242852534511 -0.00000000000000729684704543034
## 3 0.00000000004623904822395087239 -0.00000000000723512433283918869
## 4 0.00000000136880441755842640369 -0.00000000019022610209273331590
## 5 0.00000000957209961489235123481 -0.00000000117923079310976015378
## 6 0.00000003267359137095456929865 -0.00000000355740388941136121380
## Vega Rho
## 1 0.00000000000000000002262019 0.00000000000000000000134063
## 2 0.00000000011151322936226447 0.00000000001240386243492714
## 3 0.00000018658492783857876378 0.00000002935155321293390217
## 4 0.00000736457700537113689769 0.00000146215523902132945354
## 5 0.00006437594718855178712712 0.00001517417039305410167167
## 6 0.00026369053526577383413446 0.00007104986368108388969291
##
## Griegas para Put con r = -0.0284
## VencimientoDias Delta Gamma Theta
## 1 90 -1.0000000 0.00000000000000000000001681705 -0.04781587
## 2 180 -1.0000000 0.00000000000004145242852534511 -0.04830333
## 3 270 -1.0000000 0.00000000004623904822395087239 -0.04879576
## 4 360 -1.0000000 0.00000000136880441755842640369 -0.04929320
## 5 450 -1.0000000 0.00000000957209961489235123481 -0.04979572
## 6 540 -0.9999999 0.00000003267359137095456929865 -0.05030337
## Vega Rho
## 1 0.00000000000000000002262019 -151.5292
## 2 0.00000000011151322936226447 -306.1479
## 3 0.00000018658492783857876378 -463.9033
## 4 0.00000736457700537113689769 -624.8434
## 5 0.00006437594718855178712712 -789.0167
## 6 0.00026369053526577383413446 -956.4723
##
## Resultados para r = -0.0084
## [1] 0.000000000000000000000355482 0.000000000003802045938960463
## [3] 0.000000010391189526174379569 0.000000597442320220321508237
## [5] 0.000007151949112604426977979 0.000038609119829247431909813
## [1] 66.20189 67.46758 68.73706 70.01036 71.28749 72.56849
##
## Griegas para Call con r = -0.0084
## VencimientoDias Delta Gamma
## 1 90 0.0000000000000000000005488712 0.0000000000000000000008372517
## 2 180 0.0000000000030438433337385460 0.0000000000023826474807973619
## 3 270 0.0000000057363039482428898629 0.0000000030684730075726581596
## 4 360 0.0000002552908322999947761129 0.0000001048717288710587790300
## 5 450 0.0000025186182666003412650504 0.0000008466966615808916375545
## 6 540 0.0000116536247640336222859692 0.0000033367304101585545618100
## Theta Vega
## 1 -0.0000000000000000000001804251 0.000000000000000001126166
## 2 -0.0000000000004960075499935849 0.000000006409677899887669
## 3 -0.0000000006174657149901720374 0.000012381976634112723927
## 4 -0.0000000204101810989545217386 0.000564241255397869242473
## 5 -0.0000001594475152208323952665 0.005694351476018104547816
## 6 -0.0000006082590240805033629697 0.026928910810657208374508
## Rho
## 1 0.00000000000000000006947383
## 2 0.00000000076924640581303398
## 3 0.00000217107952536101391936
## 4 0.00012863731513745115019390
## 5 0.00158412259397591585231846
## 6 0.00878384333333256592246663
##
## Griegas para Put con r = -0.0084
## VencimientoDias Delta Gamma Theta
## 1 90 -1.0000000 0.0000000000000000000008372517 -0.01404206
## 2 180 -1.0000000 0.0000000000023826474807973619 -0.01408425
## 3 270 -1.0000000 0.0000000030684730075726581596 -0.01412657
## 4 360 -0.9999997 0.0000001048717288710587790300 -0.01416903
## 5 450 -0.9999975 0.0000008466966615808916375545 -0.01421174
## 6 540 -0.9999883 0.0000033367304101585545618100 -0.01425489
## Vega Rho
## 1 0.000000000000000001126166 -150.4507
## 2 0.000000006409677899887669 -301.8054
## 3 0.000012381976634112723927 -454.0683
## 4 0.000564241255397869242473 -607.2432
## 5 0.005694351476018104547816 -761.3332
## 6 0.026928910810657208374508 -916.3379
##
## Resultados para r = 0.0116
## [1] 0.00000000000000000001637953 0.00000000018641030165014185
## [3] 0.00000054024334009964878559 0.00003284161459422233614314
## [5] 0.00041463376345990399229890 0.00235551672505338038909883
## [1] 63.20360 61.47438 59.75231 58.03738 56.32990 54.63104
##
## Griegas para Call con r = 0.0116
## VencimientoDias Delta Gamma
## 1 90 0.00000000000000000002427794 0.00000000000000000003551782
## 2 180 0.00000000013792248008067687 0.00000000009943464677656261
## 3 270 0.00000026596901588613031291 0.00000012597603178401694765
## 4 360 0.00001210036756463985364689 0.00000423556857935920316348
## 5 450 0.00012193244901331139282835 0.00003364099335160887141579
## 6 540 0.00057581408750352819966162 0.00013042166993680796393922
## Theta Vega
## 1 -0.000000000000000000008325095 0.00000000000000004777412
## 2 -0.000000000024443564878118470 0.00000026749406408772667
## 3 -0.000000032445211659588653666 0.00050834153605341903751
## 4 -0.000001141811572017144651471 0.02278862528794390121534
## 5 -0.000009483846161175238194917 0.22624825257817274271055
## 6 -0.000038418219919733638946339 1.05256136570481428904600
## Rho
## 1 0.000000000000000003072766
## 2 0.000000034845961054139279
## 3 0.000100601480829031925970
## 4 0.006090735561295434509488
## 5 0.076569109970011511867582
## 6 0.433056499679891460097281
##
## Griegas para Put con r = 0.0116
## VencimientoDias Delta Gamma Theta
## 1 90 -1.0000000 0.00000000000000000003551782 0.01925340
## 2 180 -1.0000000 0.00000000009943464677656261 0.01917380
## 3 270 -0.9999997 0.00000012597603178401694765 0.01909450
## 4 360 -0.9999879 0.00000423556857935920316348 0.01901445
## 5 450 -0.9998781 0.00003364099335160887141579 0.01892749
## 6 540 -0.9994242 0.00013042166993680796393922 0.01882027
## Vega Rho
## 1 0.00000000000000004777412 -149.3799
## 2 0.00000026749406408772667 -297.5246
## 3 0.00050834153605341903751 -444.4417
## 4 0.02278862528794390121534 -590.1330
## 5 0.22624825257817274271055 -734.5475
## 6 1.05256136570481428904600 -877.4713
##
## Resultados para r = 0.0316
## [1] 0.000000000000000000645307 0.000000006724121778770155
## [3] 0.000017882612238347139755 0.000999869105908143818162
## [5] 0.011638037082184804482665 0.061098206739509386409281
## [1] 60.22665 55.56619 50.95805 46.40259 41.90791 37.50262
##
## Griegas para Call con r = 0.0316
## VencimientoDias Delta Gamma
## 1 90 0.0000000000000000009166661 0.000000000000000001283869
## 2 180 0.0000000045695906713427826 0.000000003012893697776723
## 3 270 0.0000077501630044961012491 0.000003199674029995373153
## 4 360 0.0003108556578593227532128 0.000090178139079478527636
## 5 450 0.0027685361898535832021750 0.000600385369878842552888
## 6 540 0.0115856519576267354837418 0.001951114628450584644395
## Theta Vega
## 1 -0.0000000000000000003273449 0.000000000000001726899
## 2 -0.0000000008752133200245826 0.000008105134437633038
## 3 -0.0000010571210799735255940 0.012911402179001206861
## 4 -0.0000338464693309041244262 0.485185349296653800621
## 5 -0.0002558361723930822938591 4.037815988037454673076
## 6 -0.0009437407476177218403068 15.746370054636120272562
## Rho
## 1 0.0000000000000001160093
## 2 0.0000011541105299915703
## 3 0.0029291681401478991513
## 4 0.1562464868194614053820
## 5 1.7345686115843366170708
## 6 8.6839358085759403849124
##
## Griegas para Put con r = 0.0316
## VencimientoDias Delta Gamma Theta
## 1 90 -1.0000000 0.000000000000000001283869 0.05207563
## 2 180 -1.0000000 0.000000003012893697776723 0.05149122
## 3 270 -0.9999922 0.000003199674029995373153 0.05091231
## 4 360 -0.9996891 0.000090178139079478527636 0.05030816
## 5 450 -0.9972315 0.000600385369878842552888 0.04952122
## 6 540 -0.9884143 0.001951114628450584644395 0.04827470
## Vega Rho
## 1 0.000000000000001726899 -148.3167
## 2 0.000008105134437633038 -293.3044
## 3 0.012911402179001206861 -435.0164
## 4 0.485185349296653800621 -573.3603
## 5 4.037815988037454673076 -707.1159
## 6 15.746370054636120272562 -832.3908
##
## Resultados para r = 0.0516
## [1] 0.00000000000000002174393 0.00000017884240399592912
## [3] 0.00037955162399682523811 0.01713347304656709368942
## [5] 0.16299306746661557099287 0.70832613644450503898042
## [1] 57.27088 49.74180 42.35058 35.11070 28.13243 21.68372
##
## Griegas para Call con r = 0.0516
## VencimientoDias Delta Gamma
## 1 90 0.00000000000000002954854 0.00000000000000003954386
## 2 180 0.00000011083943325383571 0.00000006628236760324226
## 3 270 0.00014254100794220813265 0.00005027773959484803839
## 4 360 0.00437339410745163532923 0.00101210851978525136034
## 5 450 0.03009542795621326927158 0.00481295406185640144148
## 6 540 0.09842133017690443685943 0.01117172417308731798002
## Theta Vega Rho
## 1 -0.00000000000000001097164 0.00000000000005318944 0.0000000000000037392
## 2 -0.00000002281868570075951 0.00017830947725282266 0.0000279827191193650
## 3 -0.00002150948352232243813 0.20288195312230442036 0.0538189914171038550
## 4 -0.00054039413722681230081 5.44544643203748535143 2.1938340553503006269
## 5 -0.00322909688075255670026 32.36891475982388044486 18.7905171119044069883
## 6 -0.00950445640288080303981 90.16082418358637085021 73.3653243346439580819
##
## Griegas para Put con r = 0.0516
## VencimientoDias Delta Gamma Theta
## 1 90 -1.0000000 0.00000000000000003954386 0.08442966
## 2 180 -0.9999999 0.00000006628236760324226 0.08288797
## 3 270 -0.9998575 0.00005027773959484803839 0.08135296
## 4 360 -0.9956266 0.00101210851978525136034 0.07934819
## 5 450 -0.9699046 0.00481295406185640144148 0.07520074
## 6 540 -0.9015787 0.01117172417308731798002 0.06749327
## Vega Rho
## 1 0.00000000000005318944 -147.2610
## 2 0.00017830947725282266 -289.1441
## 3 0.20288195312230442036 -425.7428
## 4 5.44544643203748535143 -555.1684
## 5 32.36891475982388044486 -665.1906
## 6 90.16082418358637085021 -732.4248
##
## Resultados para r = 0.0716
## [1] 0.0000000000000006268424 0.0000035169829098323675 0.0052158035357056098391
## [4] 0.1692100874380528807706 1.1938913708608751562679 3.9810112221184681402519
## [1] 54.336156 44.000032 33.930077 24.273274 15.725106 9.181064
##
## Griegas para Call con r = 0.0716
## VencimientoDias Delta Gamma
## 1 90 0.0000000000000008133219 0.000000000000001037819
## 2 180 0.0000019714339001172133 0.000001058718123157209
## 3 270 0.0016649047451189344718 0.000488762579002708958
## 4 360 0.0342555962941584121739 0.005988101500897100721
## 5 450 0.1623659930467714063163 0.017330602371953211793
## 6 540 0.3780522688918105389533 0.024482852445950629983
## Theta Vega Rho
## 1 -0.0000000000000003135557 0.000000000001395944 0.0000000000001029112
## 2 -0.0000004342329607656474 0.002848110016652712 0.0004974716697612753
## 3 -0.0002755892558474151602 1.972266602282280346 0.6277770806423821348
## 4 -0.0047444928186002712292 32.217776370123971219 17.1336884753797598080
## 5 -0.0199095190469475713524 116.554777732032349036 100.8138895005817516903
## 6 -0.0424731921465293579820 197.587598896297009787 279.1076300798737861442
##
## Griegas para Put con r = 0.0716
## VencimientoDias Delta Gamma Theta
## 1 90 -1.0000000 0.000000000000001037819 0.11632049
## 2 180 -0.9999980 0.000001058718123157209 0.11338329
## 3 270 -0.9983351 0.000488762579002708958 0.11024551
## 4 360 -0.9657444 0.005988101500897100721 0.10298625
## 5 450 -0.8376340 0.017330602371953211793 0.08510132
## 6 540 -0.6219477 0.024482852445950629983 0.05988641
## Vega Rho
## 1 0.000000000001395944 -146.2129
## 2 0.002848110016652712 -285.0424
## 3 1.972266602282280346 -416.1417
## 4 32.217776370123971219 -524.5293
## 5 116.554777732032349036 -559.1704
## 6 197.587598896297009787 -492.8782
##
## Resultados para r = 0.0916
## [1] 0.00000000000001546634 0.00005131548037204912 0.04703731860235027540
## [4] 0.99777933323131406951 4.91899911737257866662 12.30154200128674801817
## [1] 51.422316 38.339750 25.725182 14.421881 6.483455 2.388053
##
## Griegas para Call con r = 0.0916
## VencimientoDias Delta Gamma
## 1 90 0.00000000000001911954 0.00000000000002320855
## 2 180 0.00002576590364885170 0.00001227808999116819
## 3 270 0.01246248277787312050 0.00293949243441659746
## 4 360 0.15351737084419353474 0.01867615572380705233
## 5 450 0.46407698103684857927 0.02803082793670759812
## 6 540 0.74837944075140838684 0.02053563879757704450
## Theta Vega Rho
## 1 -0.000000000000007643086 0.00000000003121724 0.000000000002418971
## 2 -0.000006047712003713198 0.03302989749993816 0.006497947335135168
## 3 -0.002247545529278680444 11.86151109991004127 4.690598374831371764
## 4 -0.023619788445445068920 100.48330150600867228 76.442997655297205029
## 5 -0.064364093575746794684 188.51779353585050103 285.457453159948045140
## 6 -0.096699860468840270755 165.73181457399985561 543.038704782660715864
##
## Griegas para Put con r = 0.0916
## VencimientoDias Delta Gamma Theta
## 1 90 -1.0000000 0.00000000000002320855 0.14775310
## 2 180 -0.9999742 0.00001227808999116819 0.14299162
## 3 270 -0.9875375 0.00293949243441659746 0.13614775
## 4 360 -0.8464826 0.01867615572380705233 0.11032126
## 5 450 -0.5359230 0.02803082793670759812 0.06526607
## 6 540 -0.2516206 0.02053563879757704450 0.02875816
## Vega Rho
## 1 0.00000000003121724 -145.1723
## 2 0.03302989749993816 -280.9933
## 3 11.86151109991004127 -403.2431
## 4 100.48330150600867228 -449.9629
## 5 188.51779353585050103 -351.3719
## 6 165.73181457399985561 -196.5610
##
## Resultados para r = 0.1116
## [1] 0.0000000000003267445 0.0005580145275437404 0.2837241448033402946
## [4] 3.7013048802173216245 12.6709413411795139837 24.7192167691200097579
## [1] 48.5292159 32.7602133 17.8899875 6.7462692 1.7235646 0.3262258
##
## Griegas para Call con r = 0.1116
## VencimientoDias Delta Gamma
## 1 90 0.0000000000003839551 0.0000000000004422406
## 2 180 0.0002481309737080925 0.0001033830658964717
## 3 270 0.0606188133279724622 0.0109370183640539603
## 4 360 0.4124302230990998241 0.0307059176229693073
## 5 450 0.7894299759897787094 0.0203647235521830852
## 6 540 0.9504669219416270742 0.0065926316297945722
## Theta Vega Rho
## 1 -0.0000000000001589552 0.0000000005948467 0.00000000004857155
## 2 -0.0000618485934181563 0.2781159017604594 0.06253097785517969
## 3 -0.0118477009113252697 44.1333215238886964 22.75670540938560293
## 4 -0.0700665665400721088 165.2070171268918273 203.90881447621291045
## 5 -0.1230654799313629505 136.9603765787323368 477.90011773884151580
## 6 -0.1399769005271278288 53.2054938048829982 670.18621829030155368
##
## Griegas para Put con r = 0.1116
## VencimientoDias Delta Gamma Theta
## 1 90 -1.00000000 0.0000000000004422406 0.178732367
## 2 180 -0.99975187 0.0001033830658964717 0.171686856
## 3 270 -0.93938119 0.0109370183640539603 0.153190216
## 4 360 -0.58756978 0.0307059176229693073 0.088522775
## 5 450 -0.21057002 0.0203647235521830852 0.029327253
## 6 540 -0.04953308 0.0065926316297945722 0.006461346
## Vega Rho
## 1 0.0000000005948467 -144.13901
## 2 0.2781159017604594 -276.95151
## 3 44.1333215238886964 -376.52858
## 4 165.2070171268918273 -307.66971
## 5 136.9603765787323368 -136.58671
## 6 53.2054938048829982 -38.38594
##
## Resultados para r = 0.1316
## [1] 0.000000000005913283 0.004548632444596357 1.175888515314838401
## [4] 9.296173756511933561 23.283934811697292844 38.286009592339723895
## [1] 45.6567070 27.2633088 10.8813994 2.2543508 0.2636917 0.0209571
##
## Griegas para Call con r = 0.1316
## VencimientoDias Delta Gamma
## 1 90 0.000000000006588487 0.000000000007180477
## 2 180 0.001767286915904828 0.000632027729455780
## 3 270 0.195823118666514806 0.025175478366807873
## 4 360 0.718660851511401577 0.026612944926300987
## 5 450 0.955345833799505884 0.006645710801509730
## 6 540 0.995723176668141918 0.000810053669602347
## Theta Vega Rho
## 1 -0.000000000002821531 0.000000009658278 0.0000000008333553
## 2 -0.000466410132351616 1.700249072621177 0.4449601856546943
## 3 -0.041315701753383061 101.588700347413493 73.2354299983049088
## 4 -0.134340699101386796 143.185600320492000 351.2450688301804007
## 5 -0.166464646841954833 44.694888770564674 564.1449231020628758
## 6 -0.164814245248699726 6.537496392922745 675.5474175331087281
##
## Griegas para Put con r = 0.1316
## VencimientoDias Delta Gamma Theta
## 1 90 -1.000000000 0.000000000007180477 0.2092631692
## 2 180 -0.998232713 0.000632027729455780 0.1991889424
## 3 270 -0.804176881 0.025175478366807873 0.1491729539
## 4 360 -0.281339148 0.026612944926300987 0.0474021267
## 5 450 -0.044654166 0.006645710801509730 0.0069338928
## 6 540 -0.004276823 0.000810053669602347 0.0006231162
## Vega Rho
## 1 0.000000009658278 -143.113110
## 2 1.700249072621177 -272.639868
## 3 101.588700347413493 -317.584760
## 4 143.185600320492000 -145.923756
## 5 44.694888770564674 -28.783214
## 6 6.537496392922745 -3.298899
##
## Resultados para r = 0.1516
## [1] 0.000000000091725 0.028006704390874 3.476341496066141 17.338372091954454
## [5] 34.690966335850703 51.555747257490509
## [1] 42.8046428647 21.8638972800 5.4486007842 0.4938776463 0.0214218802
## [6] 0.0005905251
##
## Griegas para Call con r = 0.1516
## VencimientoDias Delta Gamma Theta
## 1 90 0.00000000009663308 0.0000000000993418 -0.00000000004276281
## 2 180 0.00935747802866716 0.0028053754280917 -0.00260818108948426
## 3 270 0.43499477877753506 0.0358516144341676 -0.09882694927527362
## 4 360 0.91605783231461135 0.0121590613771543 -0.18795343712811030
## 5 450 0.99525212416805997 0.0009741474177625 -0.19193326825312768
## 6 540 0.99984654456903777 0.0000380954553359 -0.18256003089619549
## Vega Rho
## 1 0.0000001336221 0.00000001222101
## 2 7.5468792707469 2.35318531747692
## 3 144.6693033060910 161.75668356073444
## 4 65.4193854698489 439.88160264238780
## 5 6.5515054421471 569.07723727010830
## 6 0.3074474089692 650.24950040826866
##
## Griegas para Put con r = 0.1516
## VencimientoDias Delta Gamma Theta
## 1 90 -0.9999999999 0.0000000000993418 0.23935031686
## 2 180 -0.9906425220 0.0028053754280917 0.22412760070
## 3 270 -0.5650052212 0.0358516144341676 0.11595912417
## 4 360 -0.0839421677 0.0121590613771543 0.01551271621
## 5 450 -0.0047478758 0.0009741474177625 0.00080956135
## 6 540 -0.0001534554 0.0000380954553359 0.00002462878
## Vega Rho
## 1 0.0000001336221 -142.0945153
## 2 7.5468792707469 -266.8581651
## 3 144.6693033060910 -220.7778800
## 4 65.4193854698489 -43.2834053
## 5 6.5515054421471 -3.0485762
## 6 0.3074474089692 -0.1180209Valoracion con la simulación de Vasicek de la tasa de interés
vasicek_simu <- function(r0, alpha, beta, sigma, T, steps) {
dt <- T / steps
rates <- numeric(steps + 1)
rates[1] <- r0
for (i in 1:steps) {
dW <- rnorm(1, mean = 0, sd = sqrt(dt))
rates[i + 1] <- rates[i] + alpha * (beta - rates[i]) * dt + sigma * sqrt(dt) * dW
}
return(rates)
}
black_scholes_merton <- function(So, K, r, VencimientoDias, sigma, Stcall, Stput, rates) {
Ano <- 252
# Definir los vencimientos a partir de un número de días establecido
VencimientoDias <- seq(from = VencimientoDias, by = 90, length.out = 6)
# Definir un conjunto de Volatilidad a partir de un valor sigma inicial
sigma <- seq(from = sigma, by = 0.05, length.out = 6)
# Cálculo del vencimiento
T <- VencimientoDias / Ano
# Definir d1 y d2
d1 <- (log(So/K) + (r + ((sigma^2)/2)) * T) / (sigma * sqrt(T))
d2 <- d1 - sigma * sqrt(T)
# Definir N1 y N2 para la posición Call y Put
Nd1 <- pnorm(d1)
Nd2 <- pnorm(d2)
Nd1P <- pnorm(-d1)
Nd2P <- pnorm(-d2)
# Valoración Call
Call <- So * Nd1 - (K * exp(-r * T) * Nd2)
# Valoración Put
Put <- (K * exp(-r * T) * Nd2P) - So * Nd1P
# Crear vector de varios precios st a partir de un stc dado
St <- seq(from = Stcall, by = 10, length.out = 90)
num_filas <- length(St)
num_columnas <- length(sigma)
# Matriz resultados de la Valoración Call
resultadosCall <- matrix(NA, nrow = num_filas, ncol = num_columnas)
for (i in 1:num_filas) {
for (j in 1:num_columnas) {
resultado <- (St[i] * pnorm((log(St[i]/K) + (r[j] + ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j]))) -
K * exp(-r[j] * T[j]) * pnorm((log(St[i]/K) + (r[j] - ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j])))) /
Call[j]
resultadosCall[i, j] <- resultado
}
}
# Definir el nombre de las columnas
colnames(resultadosCall) <- paste("Vto a", VencimientoDias, "días")
# Crear vector de varios precios st a partir de un stp dado
StP <- seq(from = Stput, by = 10, length.out = 90)
# Matriz de resultados de la valoración Put
resultadosPut <- matrix(NA, nrow = num_filas, ncol = num_columnas)
for (i in 1:num_filas) {
for (j in 1:num_columnas) {
resultado <- (K * exp(-r[j] * T[j]) * pnorm(-(log(StP[i]/K) + (r[j] - ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j]))) -
StP[i] * pnorm(-(log(StP[i]/K) + (r[j] + ((sigma[j]^2)/2)) * T[j]) / (sigma[j] * sqrt(T[j])))) /
Put[j]
resultadosPut[i, j] <- resultado
}
}
colnames(resultadosPut) <- paste("Vto a", VencimientoDias, "días")
# Incluir columna de los valores de St para la posición Call en la matriz de resultados
CallTable <- cbind(St, resultadosCall)
# Definir la tabla como un dataframe para evitar error en el tipo de datos
CallTable <- as.data.frame(CallTable)
# Proceso similar al anterior realizado ahora para la posición Put
PutTable <- cbind(StP, resultadosPut)
PutTable <- as.data.frame(PutTable)
# Graficar Call
colores <- rainbow(num_columnas)
matplot(1:num_filas, resultadosCall, type = "l", col = colores, lty = 1, xlab = "Índice", ylab = "Valor", main = "Gráfico de Líneas de Resultados Call")
legend("topleft", legend = colnames(resultadosCall), col = colores, lty = 1, cex = 0.4)
grid()
png(filename = "CallPlot.png")
dev.off()
# Graficar Put
colores <- rainbow(num_columnas)
matplot(1:num_filas, resultadosPut, type = "l", col = colores, lty = 1, xlab = "Índice", ylab = "Valor", main = "Gráfico de Líneas de Resultados Put")
legend("topright", legend = colnames(resultadosPut), col = colores, lty = 1, cex = 0.4)
grid()
png(filename = "PutPlot.png")
dev.off()
return(list(CallTable = CallTable, PutTable = PutTable))
}
r0 <- 0.05160
alpha <- 0.1
beta <- 0.05
sigma_r <- 0.01
T_vasicek <- 1 # Tiempo en años para la simulación de Vasicek
steps <- 252 # Número de pasos en la simulación de Vasicek
rates <- vasicek_simu(r0, alpha, beta, sigma_r, T_vasicek, steps)Netflix
resultado <- black_scholes_merton(So = 355.06, K = 420, r = rates, VencimientoDias = 90, sigma = sd(ret_nflx), Stcall = 360, Stput = 420, rates = rates)
print(resultado$CallTable)## St Vto a 90 días Vto a 180 días Vto a 270 días Vto a 360 días
## 1 360 587.2285 1.696572 1.205798 1.108899
## 2 370 32711260.2358 4.386834 1.710736 1.350747
## 3 380 156961127587.3486 9.807073 2.342325 1.621163
## 4 390 82220506595183.2188 19.290885 3.106482 1.919667
## 5 400 6089030434876856.0000 33.950312 4.004120 2.245391
## 6 410 87814921451840224.0000 54.312562 5.031419 2.597149
## 7 420 379464918977745344.0000 80.165991 6.180544 2.973504
## 8 430 813691581784602752.0000 110.682840 7.440651 3.372833
## 9 440 1272510054706919680.0000 144.722600 8.798999 3.793400
## 10 450 1732396788501747712.0000 181.148303 10.242018 4.233407
## 11 460 2192295173878771968.0000 219.033222 11.756222 4.691049
## 12 470 2652193591955391488.0000 257.729438 13.328898 5.164552
## 13 480 3112092010056785408.0000 296.838250 14.948582 5.652213
## 14 490 3571990428158184960.0000 336.140096 16.605299 6.152416
## 15 500 4031888846259584512.0000 375.525467 18.290647 6.663657
## 16 510 4491787264360984064.0000 414.944428 19.997746 7.184549
## 17 520 4951685682462384128.0000 454.376001 21.721096 7.713831
## 18 530 5411584100563783680.0000 493.812014 23.456405 8.250366
## 19 540 5871482518665182208.0000 533.249498 25.200387 8.793138
## 20 550 6331380936766581760.0000 572.687444 26.950574 9.341249
## 21 560 6791279354867981312.0000 612.125526 28.705146 9.893910
## 22 570 7251177772969380864.0000 651.563647 30.462778 10.450430
## 23 580 7711076191070780416.0000 691.001778 32.222524 11.010212
## 24 590 8170974609172179968.0000 730.439912 33.983713 11.572741
## 25 600 8630873027273579520.0000 769.878046 35.745880 12.137575
## 26 610 9090771445374979072.0000 809.316181 37.508701 12.704337
## 27 620 9550669863476379648.0000 848.754315 39.271958 13.272706
## 28 630 10010568281577779200.0000 888.192450 41.035502 13.842413
## 29 640 10470466699679178752.0000 927.630585 42.799233 14.413229
## 30 650 10930365117780578304.0000 967.068719 44.563086 14.984963
## 31 660 11390263535881975808.0000 1006.506854 46.327018 15.557454
## 32 670 11850161953983375360.0000 1045.944989 48.091000 16.130568
## 33 680 12310060372084774912.0000 1085.383123 49.855015 16.704196
## 34 690 12769958790186174464.0000 1124.821258 51.619050 17.278244
## 35 700 13229857208287574016.0000 1164.259393 53.383097 17.852637
## 36 710 13689755626388973568.0000 1203.697527 55.147153 18.427312
## 37 720 14149654044490373120.0000 1243.135662 56.911214 19.002216
## 38 730 14609552462591772672.0000 1282.573797 58.675278 19.577308
## 39 740 15069450880693172224.0000 1322.011931 60.439343 20.152553
## 40 750 15529349298794571776.0000 1361.450066 62.203410 20.727922
## 41 760 15989247716895971328.0000 1400.888201 63.967478 21.303392
## 42 770 16449146134997370880.0000 1440.326335 65.731546 21.878944
## 43 780 16909044553098770432.0000 1479.764470 67.495615 22.454562
## 44 790 17368942971200169984.0000 1519.202605 69.259683 23.030234
## 45 800 17828841389301569536.0000 1558.640740 71.023752 23.605949
## 46 810 18288739807402969088.0000 1598.078874 72.787821 24.181699
## 47 820 18748638225504370688.0000 1637.517009 74.551890 24.757478
## 48 830 19208536643605770240.0000 1676.955144 76.315959 25.333280
## 49 840 19668435061707169792.0000 1716.393278 78.080027 25.909100
## 50 850 20128333479808569344.0000 1755.831413 79.844096 26.484935
## 51 860 20588231897909968896.0000 1795.269548 81.608165 27.060782
## 52 870 21048130316011368448.0000 1834.707682 83.372234 27.636639
## 53 880 21508028734112768000.0000 1874.145817 85.136303 28.212504
## 54 890 21967927152214163456.0000 1913.583952 86.900372 28.788375
## 55 900 22427825570315563008.0000 1953.022086 88.664441 29.364251
## 56 910 22887723988416962560.0000 1992.460221 90.428509 29.940131
## 57 920 23347622406518362112.0000 2031.898356 92.192578 30.516014
## 58 930 23807520824619761664.0000 2071.336490 93.956647 31.091900
## 59 940 24267419242721161216.0000 2110.774625 95.720716 31.667788
## 60 950 24727317660822560768.0000 2150.212760 97.484785 32.243678
## 61 960 25187216078923960320.0000 2189.650894 99.248854 32.819569
## 62 970 25647114497025359872.0000 2229.089029 101.012923 33.395461
## 63 980 26107012915126759424.0000 2268.527164 102.776992 33.971354
## 64 990 26566911333228158976.0000 2307.965298 104.541060 34.547248
## 65 1000 27026809751329558528.0000 2347.403433 106.305129 35.123142
## 66 1010 27486708169430958080.0000 2386.841568 108.069198 35.699037
## 67 1020 27946606587532357632.0000 2426.279703 109.833267 36.274932
## 68 1030 28406505005633757184.0000 2465.717837 111.597336 36.850828
## 69 1040 28866403423735156736.0000 2505.155972 113.361405 37.426723
## 70 1050 29326301841836556288.0000 2544.594107 115.125474 38.002619
## 71 1060 29786200259937955840.0000 2584.032241 116.889543 38.578515
## 72 1070 30246098678039355392.0000 2623.470376 118.653611 39.154412
## 73 1080 30705997096140754944.0000 2662.908511 120.417680 39.730308
## 74 1090 31165895514242154496.0000 2702.346645 122.181749 40.306204
## 75 1100 31625793932343554048.0000 2741.784780 123.945818 40.882101
## 76 1110 32085692350444953600.0000 2781.222915 125.709887 41.457997
## 77 1120 32545590768546353152.0000 2820.661049 127.473956 42.033894
## 78 1130 33005489186647752704.0000 2860.099184 129.238025 42.609790
## 79 1140 33465387604749152256.0000 2899.537319 131.002093 43.185687
## 80 1150 33925286022850551808.0000 2938.975453 132.766162 43.761583
## 81 1160 34385184440951951360.0000 2978.413588 134.530231 44.337480
## 82 1170 34845082859053350912.0000 3017.851723 136.294300 44.913377
## 83 1180 35304981277154750464.0000 3057.289857 138.058369 45.489273
## 84 1190 35764879695256150016.0000 3096.727992 139.822438 46.065170
## 85 1200 36224778113357549568.0000 3136.166127 141.586507 46.641067
## 86 1210 36684676531458949120.0000 3175.604261 143.350576 47.216963
## 87 1220 37144574949560352768.0000 3215.042396 145.114644 47.792860
## 88 1230 37604473367661748224.0000 3254.480531 146.878713 48.368757
## 89 1240 38064371785763151872.0000 3293.918665 148.642782 48.944653
## 90 1250 38524270203864547328.0000 3333.356800 150.406851 49.520550
## Vto a 450 días Vto a 540 días
## 1 1.071881 1.053218
## 2 1.225649 1.164988
## 3 1.390223 1.282005
## 4 1.565240 1.404064
## 5 1.750289 1.530957
## 6 1.944916 1.662469
## 7 2.148640 1.798382
## 8 2.360961 1.938482
## 9 2.581368 2.082554
## 10 2.809350 2.230387
## 11 3.044398 2.381777
## 12 3.286016 2.536522
## 13 3.533718 2.694430
## 14 3.787041 2.855313
## 15 4.045539 3.018991
## 16 4.308789 3.185294
## 17 4.576393 3.354056
## 18 4.847976 3.525123
## 19 5.123187 3.698345
## 20 5.401700 3.873584
## 21 5.683213 4.050704
## 22 5.967446 4.229583
## 23 6.254141 4.410101
## 24 6.543062 4.592148
## 25 6.833992 4.775619
## 26 7.126734 4.960416
## 27 7.421107 5.146448
## 28 7.716948 5.333629
## 29 8.014106 5.521879
## 30 8.312448 5.711122
## 31 8.611852 5.901288
## 32 8.912206 6.092313
## 33 9.213411 6.284135
## 34 9.515379 6.476697
## 35 9.818028 6.669946
## 36 10.121286 6.863835
## 37 10.425087 7.058315
## 38 10.729374 7.253346
## 39 11.034094 7.448887
## 40 11.339200 7.644902
## 41 11.644651 7.841356
## 42 11.950408 8.038218
## 43 12.256440 8.235458
## 44 12.562714 8.433049
## 45 12.869206 8.630966
## 46 13.175891 8.829186
## 47 13.482748 9.027685
## 48 13.789757 9.226444
## 49 14.096903 9.425445
## 50 14.404170 9.624670
## 51 14.711545 9.824102
## 52 15.019015 10.023727
## 53 15.326571 10.223531
## 54 15.634202 10.423501
## 55 15.941901 10.623625
## 56 16.249660 10.823892
## 57 16.557472 11.024292
## 58 16.865332 11.224815
## 59 17.173234 11.425452
## 60 17.481173 11.626196
## 61 17.789146 11.827038
## 62 18.097148 12.027972
## 63 18.405177 12.228992
## 64 18.713229 12.430090
## 65 19.021302 12.631261
## 66 19.329394 12.832501
## 67 19.637502 13.033805
## 68 19.945625 13.235167
## 69 20.253761 13.436585
## 70 20.561909 13.638053
## 71 20.870067 13.839569
## 72 21.178234 14.041128
## 73 21.486410 14.242729
## 74 21.794593 14.444368
## 75 22.102783 14.646043
## 76 22.410978 14.847750
## 77 22.719178 15.049489
## 78 23.027384 15.251256
## 79 23.335593 15.453049
## 80 23.643806 15.654868
## 81 23.952022 15.856709
## 82 24.260241 16.058573
## 83 24.568463 16.260456
## 84 24.876687 16.462358
## 85 25.184913 16.664277
## 86 25.493141 16.866213
## 87 25.801371 17.068164
## 88 26.109602 17.270129
## 89 26.417835 17.472107
## 90 26.726068 17.674097print(resultado$PutTable)## StP
## 1 420
## 2 430
## 3 440
## 4 450
## 5 460
## 6 470
## 7 480
## 8 490
## 9 500
## 10 510
## 11 520
## 12 530
## 13 540
## 14 550
## 15 560
## 16 570
## 17 580
## 18 590
## 19 600
## 20 610
## 21 620
## 22 630
## 23 640
## 24 650
## 25 660
## 26 670
## 27 680
## 28 690
## 29 700
## 30 710
## 31 720
## 32 730
## 33 740
## 34 750
## 35 760
## 36 770
## 37 780
## 38 790
## 39 800
## 40 810
## 41 820
## 42 830
## 43 840
## 44 850
## 45 860
## 46 870
## 47 880
## 48 890
## 49 900
## 50 910
## 51 920
## 52 930
## 53 940
## 54 950
## 55 960
## 56 970
## 57 980
## 58 990
## 59 1000
## 60 1010
## 61 1020
## 62 1030
## 63 1040
## 64 1050
## 65 1060
## 66 1070
## 67 1080
## 68 1090
## 69 1100
## 70 1110
## 71 1120
## 72 1130
## 73 1140
## 74 1150
## 75 1160
## 76 1170
## 77 1180
## 78 1190
## 79 1200
## 80 1210
## 81 1220
## 82 1230
## 83 1240
## 84 1250
## 85 1260
## 86 1270
## 87 1280
## 88 1290
## 89 1300
## 90 1310
## Vto a 90 días
## 1 0.0101612182262113860675700749425232061184942722320556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 0.0004144694221170489890904153895689887576736509799957275390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 3 0.0000044485933132503455112935486503999982232926413416862487792968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 4 0.0000000124338146795141205806604911554558157149585895240306854248046875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 5 0.0000000000094101240982334284114474431959251887747086584568023681640625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 6 0.0000000000000020449765635898513541773846569071793055627495050430297851562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 7 0.0000000000000000001362300369052116102053413826400429798013647086918354034423828125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 8 0.0000000000000000000000029727233233515838437682754502588977629784494638442993164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 9 0.0000000000000000000000000000226692893062682543944656721190966663925792090594768524169921875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 10 0.0000000000000000000000000000000000642729330622437293072876651756075716548366472125053405761718750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 11 0.0000000000000000000000000000000000000000718498522118562318178325298845265933778136968612670898437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 12 0.0000000000000000000000000000000000000000000000334710243443025364656895348502985143568366765975952148437500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 13 0.0000000000000000000000000000000000000000000000000000068445913915436511912662731482726030662888661026954650878906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 14 0.0000000000000000000000000000000000000000000000000000000000006451430390987123519169754715107956144493073225021362304687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 15 0.0000000000000000000000000000000000000000000000000000000000000000000293402442288933166820302789190577641420532017946243286132812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 16 0.0000000000000000000000000000000000000000000000000000000000000000000000000006720353248822102709518488961037974149803631007671356201171875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 17 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000080703783676185599955943406058622713317163288593292236328125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 18 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000527631485678864691011430432254769584687892347574234008789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 19 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001945571818925974374309140202399248664733022451400756835937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 20 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004182555336556392952453847788873986246471758931875228881835937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 21 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000005407932335468834400202253753775494260480627417564392089843750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 22 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004330256597243897174857873988429446399095468223094940185546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 23 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002207109599870552257361647208178112578025320544838905334472656250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 24 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000734830494806129004559114292760568787343800067901611328125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 25 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000163744752239474373103206294999267811363097280263900756835937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 26 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000024986901431190918171452303164770114562998060137033462524414062500000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 27 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002668060081454874146430003567509459116990910843014717102050781250000000000000000000000000000000000000000000000000000000000000000000000000
## 28 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000203448469103468702065887208085825932357693091034889221191406250000000000000000000000000000000000000000000000000000000000000000
## 29 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011293430984470087680973313104537680828798329457640647888183593750000000000000000000000000000000000000000000000000000
## 30 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000464707366992324487310270231255060480179963633418083190917968750000000000000000000000000000000000000000000
## 31 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000014419421032087760860262992679281524033285677433013916015625000000000000000000000000000000000000
## 32 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000342889500736766845100621237119042916674516163766384124755859375000000000000000000000
## 33 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006345111620942902228102028283629465477133635431528091430664062500000000000
## 34 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000092701115934449646984252813020077610417502000927925109863281250
## 35 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001084018925509227997605252169499578940303763374686241
## 36 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010278388776533503737396074706467175019498
## 37 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000079998775948446025868369957390
## 38 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000517091435524114556
## 39 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002806539
## 40 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 41 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 42 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 43 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 44 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 45 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 46 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 47 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 48 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 49 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 50 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 51 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 52 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 53 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 54 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 55 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 56 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 57 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 58 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 59 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 60 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 61 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 62 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 63 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 64 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 65 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 66 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 67 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 68 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 69 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 70 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 71 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 72 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 73 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 74 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 75 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 76 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 77 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 78 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 79 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 80 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 81 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 82 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 83 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 84 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 85 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 86 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 87 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 88 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 89 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 90 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## Vto a 180 días
## 1 0.102345817182934339939492929261177778244018554687500000000000000000000000000
## 2 0.057087586595023602498155668172330479137599468231201171875000000000000000000
## 3 0.029701299830828118558878614408058638218790292739868164062500000000000000000
## 4 0.014419048932106687255227939203905407339334487915039062500000000000000000000
## 5 0.006539489200304256580342787685822258936241269111633300781250000000000000000
## 6 0.002775691450100150996227466038135389680974185466766357421875000000000000000
## 7 0.001105014758279031228394018171456991694867610931396484375000000000000000000
## 8 0.000413615263928976970367323851007768098497763276100158691406250000000000000
## 9 0.000145943241678996607447668654167216573114274069666862487792968750000000000
## 10 0.000048672991859575297909565327891812103189295157790184020996093750000000000
## 11 0.000015384074095366537796546191341207077130093239247798919677734375000000000
## 12 0.000004620442732668905575291184995023741066688671708106994628906250000000000
## 13 0.000001322053134770621095383028031911010202748002484440803527832031250000000
## 14 0.000000361291433662460800108583158785080513553111813962459564208984375000000
## 15 0.000000094528113529173574220917930510665883048204705119132995605468750000000
## 16 0.000000023733819129954816799961403450680563764763064682483673095703125000000
## 17 0.000000005731157057411357733447965223660958145046606659889221191406250000000
## 18 0.000000001333844764423630730116113185523829542944440618157386779785156250000
## 19 0.000000000299800713109437112291813520847938434599200263619422912597656250000
## 20 0.000000000065201450482734425993271154542441081503056921064853668212890625000
## 21 0.000000000013745796053072729594069639746933830792841035872697830200195312500
## 22 0.000000000002813979315014818992964767963016470275761093944311141967773437500
## 23 0.000000000000560301464819578704098720911552788948029046878218650817871093750
## 24 0.000000000000108679306819072872948225838563018896820722147822380065917968750
## 25 0.000000000000020565310803614866290867785325602312695991713553667068481445312
## 26 0.000000000000003801828556639783031692592096817406854825094342231750488281250
## 27 0.000000000000000687531046356521427032407189905427458143094554543495178222656
## 28 0.000000000000000121780627478167031215328802717934308930125553160905838012695
## 29 0.000000000000000021152674315545246771022580567489512759493663907051086425781
## 30 0.000000000000000003606962907742827785474368229579056333022890612483024597168
## 31 0.000000000000000000604463493731692800507021567923970906122121959924697875977
## 32 0.000000000000000000099652716677746174690072367141624454234261065721511840820
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## 34 0.000000000000000000002588461634636071877603805124756775057903723791241645813
## 35 0.000000000000000000000408548994217384126882708361705454080947674810886383057
## 36 0.000000000000000000000063661568498212243319769876315206147410208359360694885
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## 40 0.000000000000000000000000033512968937716945401310286722917908264207653701305
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## 42 0.000000000000000000000000000725217320435472961263206892468247133365366607904
## 43 0.000000000000000000000000000105358503770358146909517232936437380885763559490
## 44 0.000000000000000000000000000015190512186348859636521313465351568083860911429
## 45 0.000000000000000000000000000002174709655196651198957868977856833225814625621
## 46 0.000000000000000000000000000000309292918992639003449539314427596536916098557
## 47 0.000000000000000000000000000000043720186694621489932946478695896530553000048
## 48 0.000000000000000000000000000000006145130967427076669647167950216726239887066
## 49 0.000000000000000000000000000000000859215150731036915801586140162271476583555
## 50 0.000000000000000000000000000000000119555664077939098577721410698870840860764
## 51 0.000000000000000000000000000000000016561639974264818317602199204685575750773
## 52 0.000000000000000000000000000000000002284868022476072498515298203614065641887
## 53 0.000000000000000000000000000000000000314047743724779605985208963403465531883
## 54 0.000000000000000000000000000000000000043018187849451196727405821729206536475
## 55 0.000000000000000000000000000000000000005874471417810567104751673372931008998
## 56 0.000000000000000000000000000000000000000799977390599737236617783331382725009
## 57 0.000000000000000000000000000000000000000108668777277738303572648947969980782
## 58 0.000000000000000000000000000000000000000014728894242508315810379765364857008
## 59 0.000000000000000000000000000000000000000001992454732224813954664932591498427
## 60 0.000000000000000000000000000000000000000000269072417689830643166594426052285
## 61 0.000000000000000000000000000000000000000000036284135089315133456192019600905
## 62 0.000000000000000000000000000000000000000000004886872389222030003443075774072
## 63 0.000000000000000000000000000000000000000000000657517179854078474398465514739
## 64 0.000000000000000000000000000000000000000000000088396702231555874772206404799
## 65 0.000000000000000000000000000000000000000000000011876945448811392966673161631
## 66 0.000000000000000000000000000000000000000000000001595130420749984572533625160
## 67 0.000000000000000000000000000000000000000000000000214185299609515993361427699
## 68 0.000000000000000000000000000000000000000000000000028758147253870595005942334
## 69 0.000000000000000000000000000000000000000000000000003861733570260602520837073
## 70 0.000000000000000000000000000000000000000000000000000518708107886432708607399
## 71 0.000000000000000000000000000000000000000000000000000069702632766849559131997
## 72 0.000000000000000000000000000000000000000000000000000009371819289374776893418
## 73 0.000000000000000000000000000000000000000000000000000001260978170493479669223
## 74 0.000000000000000000000000000000000000000000000000000000169807886895031223719
## 75 0.000000000000000000000000000000000000000000000000000000022889162740765371870
## 76 0.000000000000000000000000000000000000000000000000000000003088704840070344398
## 77 0.000000000000000000000000000000000000000000000000000000000417299362775836489
## 78 0.000000000000000000000000000000000000000000000000000000000056453643150938908
## 79 0.000000000000000000000000000000000000000000000000000000000007648128211772115
## 80 0.000000000000000000000000000000000000000000000000000000000001037722500761465
## 81 0.000000000000000000000000000000000000000000000000000000000000141030224261437
## 82 0.000000000000000000000000000000000000000000000000000000000000019199423193901
## 83 0.000000000000000000000000000000000000000000000000000000000000002618469579052
## 84 0.000000000000000000000000000000000000000000000000000000000000000357788915998
## 85 0.000000000000000000000000000000000000000000000000000000000000000048984786861
## 86 0.000000000000000000000000000000000000000000000000000000000000000006720227502
## 87 0.000000000000000000000000000000000000000000000000000000000000000000923904449
## 88 0.000000000000000000000000000000000000000000000000000000000000000000127297814
## 89 0.000000000000000000000000000000000000000000000000000000000000000000017579023
## 90 0.000000000000000000000000000000000000000000000000000000000000000000002433191
## Vto a 270 días Vto a 360 días Vto a 450 días Vto a 540 días
## 1 0.25882594423400973049353979 0.414867068408448 0.54134429626 0.638048368
## 2 0.19930332911544193508213141 0.356376921382795 0.48977259544 0.594382866
## 3 0.15138391267616280178032184 0.304921910400756 0.44254851164 0.553511853
## 4 0.11346496769980686514234236 0.259906676237534 0.39939664655 0.515287260
## 5 0.08395347834698317635027109 0.220733067265357 0.36004403173 0.479564300
## 6 0.06134829586946081991793989 0.186814035914549 0.32422307009 0.446202152
## 7 0.04429501993176877122637691 0.157584624985241 0.29167391454 0.415064492
## 8 0.03161574303960872772689683 0.132510182942305 0.26214633237 0.386019895
## 9 0.02231815076645538714616990 0.111092062105495 0.23540110893 0.358942136
## 10 0.01558941417690891916014717 0.092871121951694 0.21121104579 0.333710381
## 11 0.01078020080784063833290176 0.077429390101454 0.18936160835 0.310209306
## 12 0.00738337214952501652565076 0.064390234916658 0.16965127542 0.288329144
## 13 0.00501088481116160940759263 0.053417384412127 0.15189164013 0.267965669
## 14 0.00337133077097922497986082 0.044213093716907 0.13590730693 0.249020136
## 15 0.00224959909094474275192965 0.036515723603679 0.12153562549 0.231399185
## 16 0.00148939129454030692346900 0.030096950247603 0.10862629703 0.215014703
## 17 0.00097878839463793709634032 0.024758784706068 0.09704088443 0.199783671
## 18 0.00063872611989533513866119 0.020330541847981 0.08665225274 0.185627989
## 19 0.00041404644533725817228190 0.016665863925401 0.07734396295 0.172474284
## 20 0.00026671519463953658130376 0.013639874299279 0.06900963762 0.160253715
## 21 0.00017078896153416712588163 0.011146512130090 0.06155231417 0.148901765
## 22 0.00010874957885299594358315 0.009096078907021 0.05488379809 0.138358036
## 23 0.00006887903711660541873369 0.007413012088400 0.04892402621 0.128566039
## 24 0.00004340781706305132454232 0.006033889321721 0.04360044749 0.119472992
## 25 0.00002722662928767229805925 0.004905658124322 0.03884742715 0.111029611
## 26 0.00001700132254015333688104 0.003984079966180 0.03460567832 0.103189917
## 27 0.00001057174529952610744820 0.003232373875793 0.03082172387 0.095911045
## 28 0.00000654775982548660398681 0.002620042519049 0.02744739019 0.089153052
## 29 0.00000404038402760069551272 0.002121862775762 0.02443933369 0.082878744
## 30 0.00000248446741872471108230 0.001717022822484 0.02175860016 0.077053505
## 31 0.00000152270914774668567927 0.001388388349791 0.01937021635 0.071645129
## 32 0.00000093038218752163210096 0.001121881580621 0.01724281313 0.066623671
## 33 0.00000056682650524312114216 0.000905958046264 0.01534827886 0.061961294
## 34 0.00000034439970264491036318 0.000731167492259 0.01366144160 0.057632135
## 35 0.00000020872522032468060812 0.000589786736393 0.01215977857 0.053612167
## 36 0.00000012619980162493397130 0.000475513720851 0.01082315126 0.049879080
## 37 0.00000007613468846686208069 0.000383213347707 0.00963356450 0.046412160
## 38 0.00000004583654949559570240 0.000308706935012 0.00857494768 0.043192181
## 39 0.00000002754284824807283391 0.000248598265762 0.00763295664 0.040201303
## 40 0.00000001652085608152655714 0.000200130218747 0.00679479446 0.037422972
## 41 0.00000000989325866838482386 0.000161066869852 0.00604904966 0.034841832
## 42 0.00000000591538431205461187 0.000129596739922 0.00538555038 0.032443640
## 43 0.00000000353194935634539656 0.000104253548649 0.00479523306 0.030215186
## 44 0.00000000210611734982498486 0.000083851422215 0.00427002442 0.028144221
## 45 0.00000000125439308532688465 0.000067432005490 0.00380273542 0.026219384
## 46 0.00000000074629740022699397 0.000054221357127 0.00338696616 0.024430144
## 47 0.00000000044356730085428346 0.000043594867356 0.00301702061 0.022766735
## 48 0.00000000026340049291224739 0.000035048742423 0.00268783033 0.021220104
## 49 0.00000000015628646912545748 0.000028176854375 0.00239488617 0.019781858
## 50 0.00000000009266386174405555 0.000022651967529 0.00213417717 0.018444214
## 51 0.00000000005490582421689920 0.000018210529775 0.00190213608 0.017199959
## 52 0.00000000003251461439794730 0.000014640363421 0.00169559062 0.016042403
## 53 0.00000000001924520776829087 0.000011770711432 0.00151172006 0.014965345
## 54 0.00000000001138624623080603 0.000009464194771 0.00134801644 0.013963036
## 55 0.00000000000673412672408290 0.000007610318672 0.00120225003 0.013030144
## 56 0.00000000000398155017913554 0.000006120233040 0.00107243858 0.012161726
## 57 0.00000000000235352862048833 0.000004922507368 0.00095681985 0.011353199
## 58 0.00000000000139093917942879 0.000003959725614 0.00085382728 0.010600312
## 59 0.00000000000082194356729200 0.000003185743306 0.00076206820 0.009899121
## 60 0.00000000000048567283463720 0.000002563479088 0.00068030456 0.009245970
## 61 0.00000000000028696919639880 0.000002063137299 0.00060743570 0.008637467
## 62 0.00000000000016956535460021 0.000001660777989 0.00054248306 0.008070466
## 63 0.00000000000010020031892029 0.000001337166833 0.00048457662 0.007542047
## 64 0.00000000000005921750322106 0.000001076850412 0.00043294280 0.007049501
## 65 0.00000000000003500242180642 0.000000867412897 0.00038689371 0.006590315
## 66 0.00000000000002069332573205 0.000000698878679 0.00034581760 0.006162156
## 67 0.00000000000001223666564060 0.000000563232361 0.00030917043 0.005762859
## 68 0.00000000000000723789278085 0.000000454033140 0.00027646828 0.005390413
## 69 0.00000000000000428245086586 0.000000366105028 0.00024728065 0.005042952
## 70 0.00000000000000253465048288 0.000000295288040 0.00022122458 0.004718744
## 71 0.00000000000000150073090220 0.000000238238362 0.00019795929 0.004416180
## 72 0.00000000000000088891371284 0.000000192267849 0.00017718154 0.004133765
## 73 0.00000000000000052674547021 0.000000155215133 0.00015862143 0.003870110
## 74 0.00000000000000031227574640 0.000000125342108 0.00014203873 0.003623927
## 75 0.00000000000000018521801162 0.000000101250792 0.00012721955 0.003394017
## 76 0.00000000000000010991233958 0.000000081816550 0.00011397344 0.003179265
## 77 0.00000000000000006525866982 0.000000066134467 0.00010213080 0.002978638
## 78 0.00000000000000003876754456 0.000000053476260 0.00009154056 0.002791173
## 79 0.00000000000000002304337102 0.000000043255671 0.00008206815 0.002615974
## 80 0.00000000000000001370503856 0.000000035000657 0.00007359365 0.002452212
## 81 0.00000000000000000815604322 0.000000028331044 0.00006601020 0.002299111
## 82 0.00000000000000000485681832 0.000000022940571 0.00005922255 0.002155953
## 83 0.00000000000000000289404298 0.000000018582452 0.00005314578 0.002022068
## 84 0.00000000000000000172562411 0.000000015057774 0.00004770417 0.001896833
## 85 0.00000000000000000102963313 0.000000012206163 0.00004283020 0.001779668
## 86 0.00000000000000000061478115 0.000000009898281 0.00003846362 0.001670034
## 87 0.00000000000000000036733865 0.000000008029789 0.00003455069 0.001567430
## 88 0.00000000000000000021964775 0.000000006516488 0.00003104345 0.001471386
## 89 0.00000000000000000013143369 0.000000005290412 0.00002789908 0.001381469
## 90 0.00000000000000000007870672 0.000000004296681 0.00002507938 0.001297272Ebay
resultado <- black_scholes_merton(So = 33.309, K = 45, r = rates, VencimientoDias = 90, sigma = sd(ret_ebay), Stcall = 48.5, Stput = 44.5, rates = rates)
print(resultado$CallTable)## St
## 1 48.5
## 2 58.5
## 3 68.5
## 4 78.5
## 5 88.5
## 6 98.5
## 7 108.5
## 8 118.5
## 9 128.5
## 10 138.5
## 11 148.5
## 12 158.5
## 13 168.5
## 14 178.5
## 15 188.5
## 16 198.5
## 17 208.5
## 18 218.5
## 19 228.5
## 20 238.5
## 21 248.5
## 22 258.5
## 23 268.5
## 24 278.5
## 25 288.5
## 26 298.5
## 27 308.5
## 28 318.5
## 29 328.5
## 30 338.5
## 31 348.5
## 32 358.5
## 33 368.5
## 34 378.5
## 35 388.5
## 36 398.5
## 37 408.5
## 38 418.5
## 39 428.5
## 40 438.5
## 41 448.5
## 42 458.5
## 43 468.5
## 44 478.5
## 45 488.5
## 46 498.5
## 47 508.5
## 48 518.5
## 49 528.5
## 50 538.5
## 51 548.5
## 52 558.5
## 53 568.5
## 54 578.5
## 55 588.5
## 56 598.5
## 57 608.5
## 58 618.5
## 59 628.5
## 60 638.5
## 61 648.5
## 62 658.5
## 63 668.5
## 64 678.5
## 65 688.5
## 66 698.5
## 67 708.5
## 68 718.5
## 69 728.5
## 70 738.5
## 71 748.5
## 72 758.5
## 73 768.5
## 74 778.5
## 75 788.5
## 76 798.5
## 77 808.5
## 78 818.5
## 79 828.5
## 80 838.5
## 81 848.5
## 82 858.5
## 83 868.5
## 84 878.5
## 85 888.5
## 86 898.5
## 87 908.5
## 88 918.5
## 89 928.5
## 90 938.5
## Vto a 90 días
## 1 2937011007935952768682448400006446664484008844846480244462248660004642062604022484628220004886428640004408662842846468
## 2 9732987160438000617868428828066082288464262646408228060820080804664222000068208848084444840446080024824260666424604022
## 3 16528963312940054066648266266066444246846040400644046066066864844848840446006622286022640666802264622682442842686644846
## 4 23324939465442105274620842600460040820068680680684824608428648482844664880848286466688800882680404868682422606084484884
## 5 30120915617944158722000606048484420080442462282880888604864424202848866026484804444624406660624082068660224804840408648
## 6 36916891770446212172680068486480862840226644224606446604200280422822480662044424042440202068466666088048242468202626222
## 7 43712867922948261130066860888280282246484240244860044466608244860840084826068444882842820002286462464046280448640088644
## 8 50508844075450314588644080266286064808268482646044602486066440000444008482008642260062642880040026460028806080402826208
## 9 57304820227952368036026484664282006606242664288264000468482604440800220208848682488224422608862620466000884264284026282
## 10 64100796380454421484404808242084028468020086886480668480808004680202244822480888466646242486086684460424400408026264226
## 11 70896772532956474932286008440080860220004428288666066462224200080668404480028020444866026464240686464806028640408062800
## 12 77692748685458528386668622028486608888888640880042684240820466226260488004660068462026846282662840460280444824840602484
## 13 84488724837960581824042846202482824440662886462208082222046622466662642622208226400406626000884844466862022066222402828
## 14 91284700990462635270424440800488662402846004064484880284662288806068622426040464428606400848240048262244640202400240402
## 15 98080677142964688728886666088484400064644646662664204262288424846480806844488402646026260660422062268660264484882848046
## 16 104876653295466742176668880666462626628424868868820602244484686286886060668220660684040240688684066260002842460224646620
## 17 111672629447968795624042464882488464660202080466006020226004846622688240486662808606460024426040060266624200662466284004
## 18 118468605600470849072424688460464200222462222062282828208226006682080000804400040624880804244422464262046884044888022688
## 19 125264581752972902510206802048480448884260464660448246260846248022400288608828884662804684062484468268482462020220884282
## 20 132060557905474955968288026826466284846020004228644644242048888462802448022664042686200448806840482264804020422462622666
## 21 138856534057977009416062042404482482408828246824800442224688060402224608846402280608624222628222482246246608404084060440
## 22 145652510210479044944880888060662480226802224042420248026448044244440404642086024880488262206668684866064840664664660466
## 23 152448486362981098394860002648688628888262066640686046008040286684862682446822282822402046040640688862486024662806408240
## 24 159244462515483151840644226428666064442460608248282444082640466024244822248260420844828820862002682868228686048044266624
## 25 166040438667985223200680880068488640648844464422284084244222864662220084620882660020484422840088808246242682246228246486
## 26 172836414820487258736408424624666400664028042602604280006082248804486880486846406280268440828444000860060824420808842802
## 27 179632390972989330106248088264480026862400800628646680268464286442024044426028046066824082486822806248026848628002442644
## 28 186428367125491365622266862080668082682688424806064886060224660884280200622620822266066000464268008862844080484662046660
## 29 193224343277993436002002426620482668086060284880006486222806408422866462064602462642664640022246204240860084002446028422
## 30 200020319430495472528820264246664668806044608008426682026466082664082668260204208202406668000622006866688206868026622828
## 31 206816295582997543888866864886484244004626428086468222288006820202660820600486848488402860008608242242004202066220204680
## 32 213612271735499579424684402602666000060600042204848428080866464446886288006080684248246228286444004468822462220800808086
## 33 220408247888001650784620002242446686228026802288880828242240200024462280448062424424442420642022640244888468428004828848
## 34 227204224040503686320448840848628686084200486460200224044000884426628646602624268224286888822468842460604220624684424284
## 35 234000200193005721846286684464086486064484044688820420806860262664844842802226044886020206800844204484022440880264028280
## 36 240796176345507793226206288204660262208826860662622860068440008206422006440200686260026406266222840462448446488428000042
## 37 247592152498009828742044026820042068288800248880242026860200682648648262646802422820868866486668042488866608244608604448
## 38 254388128650511900102860446660622644442226244068024666062684428086026422088086062208864066842044848464222602440802686200
## 39 261184104803013935648608064086884464202400622286644822824444006428482828284448804808608424022480040480440864246882280206
## 40 267980080955516007008824884826664420460842428260646462046084802066820882626668448282866624480068846468066868444286460068
## 41 274776057108018042544662402242846246426026006482066628888644486248086248082224280842640046666244048682282080000266066804
## 42 281572033260520113904488226082626822684442022466068068000268262846620442460444820220604286024822886460808086208422086626
## 43 288368009413022149440226860888888622640426280484488404842028646228826608666806606880488604244268046684066248062600682662
## 44 295163985565524220800046664228668208808868206862260864064468646626464828008060446064646804602646684462482244260806662424
## 45 301959961718026256320284208044840004864242864000880000806228020008680064264682242864286262688082084686800462828884268420
## 46 308755937870528327702000602880624080022668480064882640028862026606208288606846862042484462246660682464226468062280248282
## 47 315551914023030363222844646200882880682642068202402806860622400888424644062268608802228824226846882688644820820268842088
## 48 322347890175532434682668064046666466246064064280084446886042480466062648404448248086282024880420680466000826028462822840
## 49 329143866328034470122402088466844266806068642408624602648002864868288004640040084846066482800866880680428088682604428846
## 50 335939842480536505644224622268026082882442800626240842480662248260484260006446820406840860040242084608646200440682024882
## 51 342735818633038612844464808046482424202206264460208482062886466044240228420284264408268882026862262446200086088002628460
## 52 349531794785540648384286840468666624288286442688828648804846244026666484886800000068062240062008626460628208842084224266
## 53 356327770938042683924020484268848444244268000806444284666406628428662020822402846808846622082444886648042460440262820202
## 54 363123747090544719446842408680020244220262684024064444408066002820088286488804682468620080008880020662220622204440426208
## 55 369919723243046826646080602448486686640022642868022084080660200604848044002846226260068002208400268400884468846620880886
## 56 376715699395548862166804226260668406626406206086648220822220684086244600262268862020842460224846422428242680600802486822
## 57 383511675548050897726646260680842608682480888204262480684880462088260866428660808680626848264282662642420882464880082628
## 58 390307651700552933248460884402024408268464442422888642446840846480686022664466444640420206280628026666888004022068684664
## 59 397103627853054968768282846222206228222468024660402882282400220862682262820888480200004864400044286880066226886040280660
## 60 403899604005557075968042022662662660664228084488462822860604428646448440444420004002422600406684428422620006428460648288
## 61 410695580158059111588264646402846460620602646606086082606664806048864686600222640662406268426006668646088228282648244284
## 62 417491556310561147040088608804028260604686220844602224464224686440284842866644686222000426462442822660466426820620846080
## 63 424287532463063182560800222644200460660668882062246484200284064422280008402046228262080004482688062888624848684808442086
## 64 431083508615565289760668808484686822002448842882206424888484266200046266620088866084402826688208204426288428222048080604
## 65 437879484768067325282482420824868622066422424020820664624044646608462422286480402624006488608844464440666640080226682600
## 66 444675460920569360802204084626002424022826088248446826482004024084462688442806444284686646624080628664824062644208288606
## 67 451471437073071396362428008426284264628880240466062086228664804482884228688608080244660224664626268882202284402486884402
## 68 458267413225573503562286284806660686448660620284020606806882026260640006226240628046082046840246200620666060040806248220
## 69 465063389378075539184000246606842826404664882402644866662842404268040248462048260606682604880482460444044282804884844026
## 70 471859365530577574604822860048024626060628446660260028400402884644062808628464206266666882806628604662408284462066440022
## 71 478655341683079610124046484848208426066022048888886668266062662042482060884860842226240444826244864886886606426044046008
## 72 485451317835581717324404608628684888486860088088864228824662864820228828404804480028688266022884206624240282868664600646
## 73 492247293988083752886626622028866688442864640246480468680222244208648488640200422688662844048000446842608604422642206642
## 74 499043270140585788406840646860008488408868244464004600448882622604660620206626042242240002088642600666086026466624802428
## 75 505839246293087823926262600260282680404222806682620840264822002602080880462424084288246660008888860880444028024602408424
## 76 512635222445589931126422484440668042824602846420668880842040204480826048080066222080668406204408202622808628862022842062
## 77 519431198598091966688844408840240842880066448648284060608600082868848208246462264646242064220044446846286020420024468048
## 78 526227174750594002208068422242022642846060002866808202464660482264268460482280804200226222246280606660644448084402064044
## 79 533023150903096037728480684482604442842064664084424442222220840642660620648686846864820880286826846884022460048480666040
## 80 539819127055598073240644608884488242406428228202048682048280240648680862804002488820404068206062000002080862606462262646
## 81 546615103208100180440862284262464604228806206042028622626400842448426040422024026622828280402688442840844462444882600664
## 82 553411079360602215000284448664046404884260860268642804482060200804866200688442668288822448422828606664222864002860202260
## 83 560207055513104251520408460864688006288664424486268044240020600202868442224848608842406026442440846882280886666242808266
## 84 567003031665606287042860484206462806844268626604882284066680068608268082480666640806480284484680006002668208224220404262
## 85 573799007818108394242080060684448268666408664844862824644868260408044880028288888600802406668206044848422884062640862880
## 86 580594983970610429862202222886020068260002628662486006400828060464446422264004820244406682600846282668886206626628464886
## 87 587390960123112465322626246286602868826466822280602246268488428862446662400420460808480240620088842886868208664600060882
## 88 594186936275614500844888200628484608282860884008626486024448828268886842686808402864064408660628002006222626228688666868
## 89 600982912428116608044006084866462020202240822246666026662668020068622000286840620666488640846244020842000200060008420406
## 90 607778888580618643564428008208044820608602026064680268428228488424024242422266682242482808886484288662064628628406026402
## Vto a 180 días Vto a 270 días Vto a 360 días Vto a 450 días Vto a 540 días
## 1 2206409 145.3234 15.66096 6.403514 4.028152
## 2 6466470 364.1920 33.32316 11.942844 6.810371
## 3 10740462 592.5120 52.67271 18.126052 9.907890
## 4 15014454 821.0760 72.33010 24.547450 13.164871
## 5 19288446 1049.6425 92.03006 31.048269 16.499465
## 6 23562439 1278.2090 111.73507 37.574255 19.871321
## 7 27836431 1506.7754 131.44063 44.108052 23.261063
## 8 32110423 1735.3419 151.14626 50.644268 26.659455
## 9 36384415 1963.9084 170.85189 57.181238 30.062080
## 10 40658407 2192.4749 190.55752 63.718446 33.466804
## 11 44932399 2421.0414 210.26314 70.255732 36.872585
## 12 49206392 2649.6079 229.96877 76.793043 40.278908
## 13 53480384 2878.1744 249.67440 83.330363 43.685511
## 14 57754376 3106.7409 269.38003 89.867686 47.092264
## 15 62028368 3335.3074 289.08566 96.405010 50.499095
## 16 66302360 3563.8739 308.79129 102.942334 53.905970
## 17 70576353 3792.4404 328.49692 109.479658 57.312868
## 18 74850345 4021.0069 348.20255 116.016982 60.719780
## 19 79124337 4249.5734 367.90818 122.554306 64.126700
## 20 83398329 4478.1398 387.61381 129.091631 67.533623
## 21 87672321 4706.7063 407.31944 135.628955 70.940549
## 22 91946314 4935.2728 427.02507 142.166279 74.347477
## 23 96220306 5163.8393 446.73070 148.703603 77.754406
## 24 100494298 5392.4058 466.43633 155.240928 81.161335
## 25 104768290 5620.9723 486.14196 161.778252 84.568264
## 26 109042282 5849.5388 505.84759 168.315576 87.975194
## 27 113316274 6078.1053 525.55322 174.852900 91.382123
## 28 117590267 6306.6718 545.25885 181.390225 94.789053
## 29 121864259 6535.2383 564.96448 187.927549 98.195983
## 30 126138251 6763.8048 584.67010 194.464873 101.602913
## 31 130412243 6992.3713 604.37573 201.002197 105.009843
## 32 134686235 7220.9378 624.08136 207.539522 108.416773
## 33 138960228 7449.5043 643.78699 214.076846 111.823702
## 34 143234220 7678.0707 663.49262 220.614170 115.230632
## 35 147508212 7906.6372 683.19825 227.151495 118.637562
## 36 151782204 8135.2037 702.90388 233.688819 122.044492
## 37 156056196 8363.7702 722.60951 240.226143 125.451422
## 38 160330189 8592.3367 742.31514 246.763467 128.858352
## 39 164604181 8820.9032 762.02077 253.300792 132.265282
## 40 168878173 9049.4697 781.72640 259.838116 135.672212
## 41 173152165 9278.0362 801.43203 266.375440 139.079142
## 42 177426157 9506.6027 821.13766 272.912764 142.486071
## 43 181700149 9735.1692 840.84329 279.450089 145.893001
## 44 185974142 9963.7357 860.54892 285.987413 149.299931
## 45 190248134 10192.3022 880.25455 292.524737 152.706861
## 46 194522126 10420.8687 899.96018 299.062061 156.113791
## 47 198796118 10649.4352 919.66581 305.599386 159.520721
## 48 203070110 10878.0016 939.37144 312.136710 162.927651
## 49 207344103 11106.5681 959.07706 318.674034 166.334581
## 50 211618095 11335.1346 978.78269 325.211358 169.741511
## 51 215892087 11563.7011 998.48832 331.748683 173.148441
## 52 220166079 11792.2676 1018.19395 338.286007 176.555370
## 53 224440071 12020.8341 1037.89958 344.823331 179.962300
## 54 228714064 12249.4006 1057.60521 351.360656 183.369230
## 55 232988056 12477.9671 1077.31084 357.897980 186.776160
## 56 237262048 12706.5336 1097.01647 364.435304 190.183090
## 57 241536040 12935.1001 1116.72210 370.972628 193.590020
## 58 245810032 13163.6666 1136.42773 377.509953 196.996950
## 59 250084024 13392.2331 1156.13336 384.047277 200.403880
## 60 254358017 13620.7996 1175.83899 390.584601 203.810810
## 61 258632009 13849.3661 1195.54462 397.121925 207.217740
## 62 262906001 14077.9325 1215.25025 403.659250 210.624669
## 63 267179993 14306.4990 1234.95588 410.196574 214.031599
## 64 271453985 14535.0655 1254.66151 416.733898 217.438529
## 65 275727978 14763.6320 1274.36714 423.271222 220.845459
## 66 280001970 14992.1985 1294.07277 429.808547 224.252389
## 67 284275962 15220.7650 1313.77839 436.345871 227.659319
## 68 288549954 15449.3315 1333.48402 442.883195 231.066249
## 69 292823946 15677.8980 1353.18965 449.420520 234.473179
## 70 297097939 15906.4645 1372.89528 455.957844 237.880109
## 71 301371931 16135.0310 1392.60091 462.495168 241.287039
## 72 305645923 16363.5975 1412.30654 469.032492 244.693968
## 73 309919915 16592.1640 1432.01217 475.569817 248.100898
## 74 314193907 16820.7305 1451.71780 482.107141 251.507828
## 75 318467900 17049.2969 1471.42343 488.644465 254.914758
## 76 322741892 17277.8634 1491.12906 495.181789 258.321688
## 77 327015884 17506.4299 1510.83469 501.719114 261.728618
## 78 331289876 17734.9964 1530.54032 508.256438 265.135548
## 79 335563868 17963.5629 1550.24595 514.793762 268.542478
## 80 339837860 18192.1294 1569.95158 521.331086 271.949408
## 81 344111853 18420.6959 1589.65721 527.868411 275.356338
## 82 348385845 18649.2624 1609.36284 534.405735 278.763267
## 83 352659837 18877.8289 1629.06847 540.943059 282.170197
## 84 356933829 19106.3954 1648.77410 547.480384 285.577127
## 85 361207821 19334.9619 1668.47973 554.017708 288.984057
## 86 365481814 19563.5284 1688.18535 560.555032 292.390987
## 87 369755806 19792.0949 1707.89098 567.092356 295.797917
## 88 374029798 20020.6614 1727.59661 573.629681 299.204847
## 89 378303790 20249.2278 1747.30224 580.167005 302.611777
## 90 382577782 20477.7943 1767.00787 586.704329 306.018707print(resultado$PutTable)## StP
## 1 44.5
## 2 54.5
## 3 64.5
## 4 74.5
## 5 84.5
## 6 94.5
## 7 104.5
## 8 114.5
## 9 124.5
## 10 134.5
## 11 144.5
## 12 154.5
## 13 164.5
## 14 174.5
## 15 184.5
## 16 194.5
## 17 204.5
## 18 214.5
## 19 224.5
## 20 234.5
## 21 244.5
## 22 254.5
## 23 264.5
## 24 274.5
## 25 284.5
## 26 294.5
## 27 304.5
## 28 314.5
## 29 324.5
## 30 334.5
## 31 344.5
## 32 354.5
## 33 364.5
## 34 374.5
## 35 384.5
## 36 394.5
## 37 404.5
## 38 414.5
## 39 424.5
## 40 434.5
## 41 444.5
## 42 454.5
## 43 464.5
## 44 474.5
## 45 484.5
## 46 494.5
## 47 504.5
## 48 514.5
## 49 524.5
## 50 534.5
## 51 544.5
## 52 554.5
## 53 564.5
## 54 574.5
## 55 584.5
## 56 594.5
## 57 604.5
## 58 614.5
## 59 624.5
## 60 634.5
## 61 644.5
## 62 654.5
## 63 664.5
## 64 674.5
## 65 684.5
## 66 694.5
## 67 704.5
## 68 714.5
## 69 724.5
## 70 734.5
## 71 744.5
## 72 754.5
## 73 764.5
## 74 774.5
## 75 784.5
## 76 794.5
## 77 804.5
## 78 814.5
## 79 824.5
## 80 834.5
## 81 844.5
## 82 854.5
## 83 864.5
## 84 874.5
## 85 884.5
## 86 894.5
## 87 904.5
## 88 914.5
## 89 924.5
## 90 934.5
## Vto a 90 días
## 1 0.00868357498733376628741176261883083498105406761169433593750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 0.00000000000000000000000000000000000000000000000000000000000000000015981159020085773745517565558316164242569357156753540039062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 3 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006345296
## 4 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 5 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 6 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 7 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 8 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 9 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 10 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 11 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 12 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 13 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 14 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 15 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 16 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 17 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 18 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 19 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 20 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 21 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 22 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 23 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 24 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 25 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 26 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 27 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 28 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 29 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 30 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 31 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 32 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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## 38 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 39 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 40 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 41 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 42 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 43 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 44 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 45 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 46 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 47 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 48 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 49 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 50 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 51 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 52 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 53 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 54 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 55 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 56 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 57 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 58 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 59 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 60 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 61 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 62 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 63 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 64 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 65 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 66 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 67 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 68 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 69 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 70 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 71 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 72 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 73 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 74 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 75 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 76 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 77 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 78 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 79 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 80 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 81 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 82 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 83 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 84 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 85 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 86 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 87 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 88 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 89 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 90 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## Vto a 180 días
## 1 0.0573948587590920392131899063770106295123696327209472656250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 2 0.0000044344941716037496151799068844212570184026844799518585205078125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 3 0.0000000000006907181908911212038504334742583523620851337909698486328125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 4 0.0000000000000000000024380743976055313266149832118756535237480420619249343872070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 5 0.0000000000000000000000000000009519483660604650636719026302046131604583933949470520019531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 6 0.0000000000000000000000000000000000000001071692298896024937954023215080923137065838091075420379638671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 7 0.0000000000000000000000000000000000000000000000000062748829801832854248869186797321617632405832409858703613281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 8 0.0000000000000000000000000000000000000000000000000000000000002772808872117692149429635239954450298682786524295806884765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 9 0.0000000000000000000000000000000000000000000000000000000000000000000000117514203951759955480739494593223071206011809408664703369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 10 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000005583946900361241891513203183805558182939421385526657104492187500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 11 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000329506725971445497383634226640225506343995220959186553955078125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 12 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000025808380033714973327517439027900536530069075524806976318359375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 13 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002799651604491537565215508731597537916968576610088348388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 14 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000431763495761157038146590969596161357912933453917503356933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 15 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000096077800119296150041167670075026308040833100676536560058593750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 16 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000031063843772172396438292774067946311333798803389072418212890625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 17 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000014614350015185753471798346669885404480737634003162384033203125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 18 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009980983201052933457934901451125142557430081069469451904296875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 19 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009846118223581676981784327473690154874930158257484436035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## 20 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013934724714479086196683432774534594500437378883361816406250000000000000000000000000000000000000000000000000000000000000000000000000000000
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## 80 0.000000000000000000000000474066274 0.0000000000000091769142
## 81 0.000000000000000000000000312987383 0.0000000000000072771009
## 82 0.000000000000000000000000207325768 0.0000000000000057813840
## 83 0.000000000000000000000000137782088 0.0000000000000046015305
## 84 0.000000000000000000000000091858706 0.0000000000000036690668
## 85 0.000000000000000000000000061434412 0.0000000000000029307444
## 86 0.000000000000000000000000041213861 0.0000000000000023450701
## 87 0.000000000000000000000000027732699 0.0000000000000018796464
## 88 0.000000000000000000000000018716984 0.0000000000000015091285
## 89 0.000000000000000000000000012669302 0.0000000000000012136505
## 90 0.000000000000000000000000008600454 0.0000000000000009776115Estrategias
Netflix
prome_nflx## [1] 420.0369st_netflix <- 355.06
st_1_netflix <- -415.207115
k_netflix <- 300
#Largo en la acción
largo_accion_n <- (st_netflix + st_1_netflix) + st_1_netflix
print(largo_accion_n)## [1] -475.3542#largo en la call
largo_call_n <- max((st_netflix - k_netflix), 0)
print(largo_call_n)## [1] 55.06#Corto en la put
corto_put_n <- -max((k_netflix - st_netflix), 0)
print(corto_put_n)## [1] 0Ebay
prome_ebay## [1] 47.10313st_ebay <- 33.309
st_1_ebay <- -50.709305
k_ebay <- 30
#Largo en la acción
largo_accion_e <- (st_ebay + st_1_ebay) + st_1_ebay
print(largo_accion_e)## [1] -68.10961#largo en la call
largo_call_e <- max((st_ebay - k_ebay), 0)
print(largo_call_e)## [1] 3.309#Corto en la put
corto_put_e <- -max((k_ebay - st_ebay), 0)
print(corto_put_e)## [1] 0PyG
Netflix
PyG_Netflix <- bsm$NFLX + (largo_accion_n + largo_call_n + corto_put_n)
PyG_Netflix## [1] -65.234232 -71.104228 -68.444224 -77.014231 -83.664225 -66.894236
## [7] -64.564219 -63.164225 -59.424235 -68.284220 -69.024241 -74.734232
## [13] -76.864237 -80.564219 -69.674235 -63.174235 -56.774241 -55.084239
## [19] -51.084239 -49.254221 -59.994242 -58.094218 -50.274241 -52.974223
## [25] -45.694224 -44.864237 -38.574229 -39.744242 -44.134226 -40.364237
## [31] -39.294230 -40.794230 -47.044230 -53.694224 -54.304240 -57.854228
## [37] -95.084239 -105.194224 -109.674235 -112.994242 -102.354228 -93.834239
## [43] -84.514231 -87.594218 -94.364237 -97.304240 -100.794230 -101.464243
## [49] -112.664225 -110.194224 -116.004221 -104.394236 -111.364237 -109.464243
## [55] -108.014231 -121.184245 -124.534220 -117.494242 -110.914225 -121.304240
## [61] -122.484232 -123.364237 -128.854228 -125.314219 -129.264231 -128.524241
## [67] -123.514231 -126.544230 -131.004221 -128.774241 -127.044230 -130.124217
## [73] -125.954234 -132.304240 -132.024241 -131.434245 -126.144236 -126.004221
## [79] -121.694224 -128.734232 -133.694224 -149.544230 -154.374217 -165.704234
## [85] -155.544230 -156.984232 -157.214243 -152.674235 -150.714243 -152.264231
## [91] -152.144236 -147.504221 -145.834239 -149.574229 -152.764231 -139.814219
## [97] -137.364237 -134.764231 -136.044230 -134.014231 -126.944224 -144.994242
## [103] -142.244242 -153.604228 -149.024241 -148.794230 -143.474223 -138.434245
## [109] -139.084239 -128.844218 -132.884226 -133.484232 -127.434245 -132.264231
## [115] -131.704234 -130.724223 -128.724223 -126.114237 -128.284220 -137.184245
## [121] -130.674235 -125.264231 -117.724223 -117.694224 -115.134226 -108.604228
## [127] -109.814219 -104.744242 -107.804240 -104.364237 -105.634226 -110.304240
## [133] -114.134226 -115.974223 -117.434245 -112.944224 -117.794230 -127.174235
## [139] -121.364237 -121.854228 -121.794230 -116.084239 -104.814219 -99.494242
## [145] -88.074229 -83.394236 -87.194224 -87.094218 -87.664225 -91.204234
## [151] -96.984232 -96.724223 -90.484232 -94.394236 -84.464243 -89.544230
## [157] -81.034220 -84.634226 -91.244242 -81.374217 -81.604228 -81.224223
## [163] -81.674235 -80.624217 -82.184245 -94.294230 -70.694224 -67.134226
## [169] -77.414225 -71.774241 -77.134226 -72.554240 -75.204234 -62.294230
## [175] -51.284220 -50.624217 -53.344218 -53.524241 -49.224223 -46.604228
## [181] -40.284220 -38.894236 -39.894236 -32.514231 -34.104228 -34.294230
## [187] -40.224223 -51.594218 -60.204234 -41.054240 -48.584239 -51.264231
## [193] -39.244242 -51.524241 -36.504221 -47.514231 -51.324229 -73.804240
## [199] -56.164225 -70.374217 -105.044230 -83.994242 -121.454234 -100.544230
## [205] -104.824229 -88.264231 -87.464243 -60.024241 -62.974223 -77.904215
## [211] -57.304240 -63.174235 -49.334239 -44.794230 -56.214243 -50.214243
## [217] -58.534220 -40.334239 -48.014231 -49.174235 -49.574229 -23.574229
## [223] -6.744242 6.455770 18.875783 2.665761 17.195760 13.535757
## [229] 1.125783 6.405782 4.695760 1.085775 -16.464243 -8.404215
## [235] -0.444224 -5.024241 7.855764 4.385763 13.965780 16.235769
## [241] 15.255758 20.225759 11.525777 17.975759 21.655782 33.895772
## [247] 32.285757 30.745779 27.375783 15.955770 9.025777 -5.524241
## [253] -0.404215 -6.854228 -0.564219 5.625783 7.015768 1.675771
## [259] -5.964243 -0.694224 -0.804240 13.755758 14.185781 5.265768
## [265] -2.224223 5.205770 15.835775 27.475759 29.575765 33.425771
## [271] 47.745779 45.965780 37.555776 45.615774 23.105764 26.945760
## [277] 34.745779 65.345785 56.595785 73.515768 72.865774 82.485769
## [283] 87.465780 128.435750 105.205770 104.585775 102.965780 107.095785
## [289] 72.695760 82.115774 69.805776 69.525777 57.285757 60.155782
## [295] 75.355764 68.215780 64.185781 65.505758 68.585775 78.325765
## [301] 89.345785 81.815755 88.785757 74.435781 63.085775 46.635763
## [307] 55.175771 61.035757 62.385763 62.055776 71.575765 64.235769
## [313] 77.605764 72.015768 68.515768 70.285757 127.235799 105.975790
## [319] 103.595785 109.265768 136.255758 132.545797 105.455770 95.755758
## [325] 86.725759 79.895772 60.375783 61.735769 55.965780 75.695760
## [331] 63.565755 49.905782 49.665761 67.055776 70.875783 50.315755
## [337] 52.785757 62.585775 70.355764 73.185781 79.735769 107.215780
## [343] 82.765768 100.355794 85.575765 114.365743 111.495748 119.145772
## [349] 119.515768 133.795797 121.155782 121.645772 110.495748 110.425741
## [355] 105.125753 68.755758 64.935781 67.985769 67.945760 68.635763
## [361] 65.945760 83.915761 55.445760 63.825765 66.925771 76.655782
## [367] 93.465780 94.435750 50.205770 59.945760 70.465780 66.475759
## [373] 62.545766 58.805776 60.335775 61.495779 64.375783 67.945760
## [379] 56.325765 62.585775 64.705770 71.065755 70.405782 84.285757
## [385] 83.085775 77.225759 78.015768 95.485799 92.365743 73.305776
## [391] 80.795766 82.925771 102.125753 99.485799 104.535787 112.605794
## [397] 114.155782 108.615743 107.035787 94.185750 93.675741 98.825765
## [403] 110.575765 104.295797 120.435750 102.565755 100.505758 80.195760
## [409] 88.595785 90.105764 78.805776 73.955770 87.495779 80.565755
## [415] 77.685781 81.475759 166.045797 159.545797 144.875753 136.485799
## [421] 141.635763 102.985799 118.305746 112.095785 118.745748 127.865743
## [427] 119.155782 131.865743 130.495748 127.625753 138.775777 143.295797
## [433] 137.295797 136.225790 136.985799 131.045797 127.925741 119.925741
## [439] 113.485799 125.855794 133.115743 126.405782 118.555746 130.345785
## [445] 127.525777 100.405782 90.995779 96.095785 73.035757 86.145772
## [451] 84.245779 102.765768 97.725790 99.955770 103.735799 104.145772
## [457] 84.495779 91.885763 102.815755 114.795797 100.515768 82.565755
## [463] 87.755758 93.655782 93.095785 101.365743 119.125753 120.375753
## [469] 124.235799 126.695760 134.285787 135.015768 132.485799 133.435750
## [475] 119.725790 128.925741 126.245748 134.145772 129.275777 88.605764
## [481] 88.485769 85.255758 90.005758 85.255758 86.225759 88.705770
## [487] 93.175741 88.815755 82.885763 75.785757 79.255758 83.545766
## [493] 66.395772 74.785757 64.685781 66.365774 73.075765 68.645772
## [499] 65.985769 67.405782 81.375783 77.595785 82.605764 81.045766
## [505] 82.065755 83.565755 82.515768 78.785757 78.945760 69.135763
## [511] 74.445760 74.365774 72.095785 65.515768 66.975759 68.475759
## [517] 79.595785 71.605764 72.115774 78.045766 80.475759 76.705770
## [523] 88.525777 92.445760 97.765768 106.775777 112.735799 113.205770
## [529] 107.915792 113.245748 113.685750 121.345785 115.665792 110.465780
## [535] 115.685750 117.015768 120.385763 127.655782 122.655782 110.015768
## [541] 111.985799 110.755758 93.335775 91.475759 95.115743 96.195760
## [547] 98.615743 99.005758 93.955770 97.275777 94.855794 90.525777
## [553] 97.055746 104.595785 100.255758 99.675741 95.545797 92.105794
## [559] 90.425771 95.625753 97.625753 98.615743 101.575765 123.415792
## [565] 126.585775 133.035787 133.115743 127.285787 129.825765 138.625753
## [571] 145.885763 148.895772 161.775777 168.255758 170.235799 186.415792
## [577] 185.755758 177.245748 178.425741 168.995748 157.465780 162.575765
## [583] 166.205770 169.055746 155.135763 152.845785 170.355794 172.965780
## [589] 172.095785 172.345785 163.555746 178.765768 190.045797 192.855794
## [595] 183.055746 214.515768 218.805746 211.555746 212.365743 206.745748
## [601] 204.645772 209.465780 213.505758 207.995748 217.675741 218.705770
## [607] 204.845785 232.865743 244.485799 251.365743 248.225790 242.625753
## [613] 253.755758 270.015768 260.875753 257.425741 267.995748 248.105794
## [619] 225.425741 231.155782 235.695760 226.615743 237.285787 262.315755
## [625] 259.035787 267.105794 271.395772 261.725790 258.505758 238.905782
## [631] 233.765768 237.995748 245.345785 243.545797 221.605794 197.475790
## [637] 196.175741 181.835775 192.395772 205.285787 207.785787 190.705770
## [643] 191.365743 184.265768 177.695760 184.745748 170.765768 166.435750
## [649] 173.445760 184.625753 193.945760 193.795797 192.825765 190.415792
## [655] 190.245748 191.795797 182.145772 177.075765 170.855794 147.225790
## [661] 132.995748 120.765768 119.555746 120.545797 116.925741 98.905782
## [667] 105.395772 90.505758 95.565755 87.955770 -22.794230 -33.144236
## [673] -53.874217 -60.594218 -33.594218 -35.934245 6.845785 36.835775
## [679] 9.185781 -14.694224 -10.124217 -18.194224 -16.764231 -7.404215
## [685] -14.024241 -28.984232 -23.724223 -12.834239 -22.214243 -33.624217
## [691] -29.004221 -42.914225 -52.834239 -30.264231 -29.494242 -25.774241
## [697] -34.054240 -40.264231 -52.224223 -58.564219 -70.034220 -78.534220
## [703] -61.504221 -63.524241 -79.974223 -89.284220 -76.544230 -62.764231
## [709] -48.894236 -39.694224 -45.704234 -37.374217 -45.804240 -44.584239
## [715] -46.444224 -41.784220 -28.474223 -38.824229 -45.704234 -46.824229
## [721] -28.794230 -40.144236 -51.944224 -58.144236 -64.414225 -72.294230
## [727] -76.194224 -69.864237 -79.164225 -82.434245 -71.684245 -194.104228
## [733] -202.074229 -204.774226 -210.384226 -221.894236 -231.754237 -220.774226
## [739] -229.934229 -220.834223 -220.424235 -216.284235 -231.974223 -239.324229
## [745] -247.194224 -242.634226 -253.924235 -245.984232 -232.654231 -233.784235
## [751] -229.734232 -243.104228 -236.814234 -233.944224 -232.854228 -239.954234
## [757] -232.464228 -228.894236 -225.104228 -222.854228 -227.384226 -215.204234
## [763] -221.314234 -223.154231 -221.684229 -217.464228 -227.524226 -237.354228
## [769] -250.604228 -252.754237 -240.184229 -246.944224 -244.784235 -249.384226
## [775] -241.404231 -238.584223 -229.444224 -231.154231 -240.694224 -241.934229
## [781] -245.424235 -240.344233 -234.414225 -236.234232 -231.024226 -233.314234
## [787] -242.954234 -245.844233 -243.734232 -245.514231 -231.184229 -229.374232
## [793] -218.664225 -203.854228 -196.414225 -199.854228 -201.784235 -206.384226
## [799] -193.544230 -194.274226 -195.394236 -194.084223 -198.874232 -193.564234
## [805] -190.384226 -193.514231 -186.804225 -190.354228 -176.184229 -177.594233
## [811] -170.994227 -171.184229 -174.604228 -179.144236 -175.124232 -179.134226
## [817] -193.754237 -195.744227 -190.684229 -186.314234 -197.014231 -195.724223
## [823] -199.644236 -196.734232 -190.254237 -194.184229 -201.904231 -191.334223
## [829] -192.854228 -186.724223 -183.764231 -202.164225 -196.174235 -184.914225
## [835] -180.164225 -176.664225 -177.444224 -183.424235 -183.244227 -193.884226
## [841] -196.224223 -195.934229 -175.094233 -180.584223 -184.854228 -181.254237
## [847] -179.554225 -183.564234 -180.274226 -195.544230 -190.314234 -206.004237
## [853] -199.424235 -187.784235 -190.294230 -175.194224 -179.434229 -147.914225
## [859] -152.134226 -130.724223 -137.844218 -129.274241 -121.674235 -123.354228
## [865] -124.574229 -128.414225 -133.544230 -147.294230 -151.234232 -159.504221
## [871] -161.694224 -156.834239 -165.634226 -145.324229 -130.164225 -121.024241
## [877] -110.094218 -114.274241 -125.014231 -132.314219 -135.244242 -133.604228
## [883] -128.794230 -134.754221 -139.124217 -139.334239 -114.764231 -103.344218
## [889] -99.884226 -107.704234 -114.734232 -111.874217 -110.034220 -100.284220
## [895] -105.114237 -99.954234 -102.464243 -129.884226 -129.584239 -131.994242
## [901] -132.104228 -122.334239 -122.544230 -125.334239 -136.124217 -143.414225
## [907] -129.174235 -125.414225 -125.344218 -110.884226 -110.594218 -104.744242
## [913] -105.124217 -92.754221 -93.034220 -90.164225 -87.474223 -94.074229
## [919] -93.964243 -104.514231 -77.794230 -62.874217 -56.464243 -52.334239
## [925] -55.424235 -59.524241 -67.184245 -66.434245 -58.304240 -53.404215
## [931] -54.394236 -58.814219 -57.344218 -53.464243 -57.794230 -72.934245
## [937] -61.724223 -60.334239 -58.874217 -69.584239 -72.334239 -82.794230
## [943] -85.414225 -96.644236 -103.144236 -97.264231 -98.164225 -106.814219
## [949] -108.414225 -105.114237 -108.264231 -111.824229 -108.504221 -122.514231
## [955] -127.534220 -126.784220 -125.354228 -116.504221 -110.234232 -116.794230
## [961] -115.164225 -114.504221 -126.394236 -99.924235 -91.904215 -92.634226
## [967] -96.774241 -88.264231 -81.864237 -74.814219 -72.014231 -73.544230
## [973] -77.944224 -80.964243 -81.304240 -82.084239 -89.264231 -74.104228
## [979] -81.664225 -87.574229 -86.594218 -97.174235 -94.944224 -92.314219
## [985] -91.274241 -97.744242 -99.144236 -94.444224 -90.364237 -96.174235
## [991] -102.744242 -100.994242 -99.514231 -97.534220 -89.084239 -88.154215
## [997] -84.874217 -75.534220 -80.404215 -84.404215 -86.544230 -80.334239
## [1003] -49.004221 -54.934245 -57.284220 -64.304240 -55.444224 -61.294230
## [1009] -41.414225 -27.314219 -25.064219 -17.164225 -19.824229 -16.754221
## [1015] -21.004221 -20.524241 -10.924235 -0.274241 3.675771 15.435781
## [1021] 20.565755 24.975759 11.665761 14.405782 4.155782 2.185781
## [1027] 3.725759 -4.354228 -3.214243 9.545766 7.945760 20.195760
## [1033] 21.145772 25.605764 18.545766 17.805776 21.415761 19.915761
## [1039] 23.755758 30.085775 21.615774 29.755758 54.505758 57.295766
## [1045] 17.125783 7.205770 8.075765 7.405782 2.375783 -7.124217
## [1051] 5.485769 18.675771 18.325765 9.405782 10.705770 11.305776
## [1057] 20.465780 18.005758 8.605764 9.685781 1.365774 7.485769
## [1063] 3.405782 -4.844218 -17.294230 -15.764231 -12.004221 -7.124217
## [1069] 7.255758 -13.364237 -4.264231 -2.234232 9.695760 14.375783
## [1075] 13.385763 19.585775 28.385763 25.465780 22.845785 22.505758
## [1081] 25.065755 14.395772 -8.054240 -19.804240 -23.354228 -25.894236
## [1087] -24.094218 -33.994242 -36.144236 -40.484232 -35.494242 -41.044230
## [1093] -42.704234 -43.934245 -42.694224 -39.964243 -43.544230 -43.394236
## [1099] -47.704234 -38.784220 -34.344218 -46.974223 -54.364237 -59.094218
## [1105] -64.614237 -59.474223 -64.574229 -74.104228 -18.524241 -19.334239
## [1111] -13.454234 -6.564219 -9.044230 -16.754221 -22.424235 -10.214243
## [1117] -8.604228 -0.104228 4.415761 12.065755 14.445760 14.315755
## [1123] 16.355764 14.855764 26.945760 24.325765 28.355764 41.645772
## [1129] 46.655782 45.615774 54.175771 54.655782 57.705770 59.265768
## [1135] 58.875783 58.705770 56.895772 53.675771 45.445760 33.605764
## [1141] 34.855764 26.435781 31.705770 33.465780 39.595785 42.705770
## [1147] 59.685781 49.535757 51.765768 65.825765 74.725759 68.975759
## [1153] 71.315755 66.465780 70.895772 71.495779 70.215780 66.585775
## [1159] 48.205770 49.965780 54.375783 53.765768 64.735769 61.795766
## [1165] 58.035757 71.935781 71.865774 60.945760 60.035757 65.015768
## [1171] 62.655782 65.415761 71.895772 124.575765 141.705770 150.125753
## [1177] 155.495748 142.555746 143.815755 147.215780 144.345785 141.765768
## [1183] 135.585775 139.005758 138.235799 141.025777 137.555746 134.225790
## [1189] 159.035787 173.165792 163.655782 154.835775 153.055746 168.175741
## [1195] 163.265768 167.355794 181.375753 176.185750 182.625753 199.045797
## [1201] 195.535787 178.205770 177.395772 188.215780 184.525777 180.635763
## [1207] 190.785787 189.155782 192.715780 185.585775 198.095785 200.445760
## [1213] 207.395772 202.415792 207.715780 207.165792 208.945760 193.235799
## [1219] 187.035787 194.015768 193.915792 209.785787 196.845785 215.885763
## [1225] 208.115743 197.905782 198.285787 208.485799 202.535787 186.855794
## [1231] 197.225790 193.395772 190.265768 134.745748 134.305746 157.455770
## [1237] 134.825765 144.505758 140.935750 139.195760 130.345785 131.415792
## [1243] 144.855794 159.045797 176.675741 185.705770 189.175741 191.795797
## [1249] 190.575765 196.295797 193.365743 193.225790 190.225790 200.805746
## [1255] 220.525777 230.315755 220.175741 215.375753 226.455770Ebay
PyG_Ebay <- bsm$EBAY + (largo_accion_e + largo_call_e + corto_put_e)
PyG_Ebay## [1] -31.491269 -31.601624 -31.213879 -31.629322 -31.915532 -31.066163
## [7] -31.047699 -30.816903 -30.170647 -29.607480 -29.505921 -28.776577
## [13] -28.795044 -28.878136 -28.785809 -28.176484 -27.751801 -27.945687
## [19] -27.825665 -28.139561 -28.776577 -28.610398 -28.527310 -28.333432
## [25] -27.973381 -27.797970 -27.964146 -28.056473 -28.296505 -27.927220
## [31] -27.862584 -28.241112 -27.816422 -27.622551 -27.945687 -28.767350
## [37] -28.084153 -27.677948 -27.253258 -26.920906 -26.920906 -27.124016
## [43] -26.736260 -26.422375 -26.597786 -26.773186 -26.856286 -27.336346
## [49] -28.970444 -28.158013 -28.130326 -26.717797 -27.585625 -28.111866
## [55] -26.967068 -28.204182 -28.388825 -27.853348 -27.511765 -27.844120
## [61] -27.521008 -27.871819 -29.072007 -28.425755 -28.795044 -27.788735
## [67] -27.382515 -27.475155 -27.984688 -28.077328 -27.002682 -27.401047
## [73] -26.446835 -27.493687 -27.836461 -27.475155 -27.401047 -27.465901
## [79] -27.252819 -27.410302 -27.373257 -27.410302 -27.521477 -28.151444
## [85] -28.447903 -28.744358 -29.253888 -28.688767 -29.096390 -29.439179
## [91] -29.642983 -29.309468 -29.763413 -30.226628 -29.735627 -29.661503
## [97] -29.087132 -29.263150 -28.781411 -28.744358 -28.586873 -28.836998
## [103] -28.429379 -28.725827 -28.484951 -31.801552 -31.597718 -31.505078
## [109] -31.347596 -31.579197 -32.144322 -32.144322 -31.996087 -31.931240
## [115] -31.912713 -32.477826 -32.246224 -32.144322 -32.311066 -32.709431
## [121] -32.412980 -32.125786 -32.283284 -32.320332 -32.505616 -32.431504
## [127] -32.264744 -31.588456 -31.681107 -31.588456 -31.765164 -32.341809
## [133] -32.481316 -32.276703 -32.444107 -32.379006 -32.648724 -32.509217
## [139] -32.323204 -31.960484 -31.802376 -31.876778 -31.411751 -31.653565
## [145] -31.281552 -31.142033 -31.123436 -31.123436 -31.086232 -31.253643
## [151] -31.504757 -31.216435 -31.039730 -31.355957 -31.523365 -31.672173
## [157] -31.690777 -32.081379 -32.351105 -32.499913 -31.923291 -31.941883
## [163] -31.393151 -31.486149 -31.579163 -31.421055 -31.681454 -31.913975
## [169] -31.802376 -31.123436 -32.639420 -32.192986 -33.588076 -32.816138
## [175] -30.007374 -30.267785 -29.458641 -31.132733 -31.300145 -30.909527
## [181] -30.249188 -30.211991 -29.328431 -29.579552 -29.895768 -29.746952
## [187] -29.272633 -30.146878 -30.890919 -30.677018 -32.211602 -32.435830
## [193] -31.202530 -30.492451 -28.838707 -30.025288 -30.800778 -31.613633
## [199] -31.127789 -32.258309 -33.940089 -33.043139 -34.678194 -33.706513
## [205] -35.556454 -37.144797 -39.032118 -40.190672 -38.948031 -38.294009
## [211] -36.621579 -36.602894 -35.659232 -36.715012 -37.910939 -37.527867
## [217] -37.322312 -35.668572 -35.257475 -33.958777 -33.192627 -32.323719
## [223] -31.408078 -30.987641 -30.025288 -29.801056 -29.632882 -29.660916
## [229] -29.062951 -29.380612 -28.035195 -27.773587 -28.287457 -28.334179
## [235] -27.586728 -28.128624 -27.586728 -27.128907 -26.540280 -26.147870
## [241] -25.419102 -25.437790 -25.559258 -25.951657 -25.521885 -25.456482
## [247] -25.092087 -25.185521 -24.895890 -25.120125 -24.204495 -24.288582
## [253] -23.550465 -23.475731 -22.097287 -22.416104 -21.684700 -21.243973
## [259] -18.515236 -19.021599 -19.115376 -18.149529 -18.618386 -19.846783
## [265] -20.109345 -19.893670 -19.678002 -19.387303 -19.377938 -19.518586
## [271] -18.702782 -18.102646 -19.068489 -18.477726 -17.080536 -16.686699
## [277] -15.617711 -15.139485 -13.826680 -12.129433 -11.351128 -10.160233
## [283] -9.269413 -9.222527 -10.132111 -9.400692 -10.047722 -9.803910
## [289] -10.291523 -9.972702 -11.735596 -11.970021 -13.085896 -13.114033
## [295] -11.135460 -11.960644 -13.667271 -13.489109 -12.964001 -11.754345
## [301] -11.979393 -11.669945 -13.151524 -13.029637 -13.817311 -13.892327
## [307] -12.767071 -12.026280 -12.016907 -11.022938 -11.322995 -10.685357
## [313] -10.732247 -10.216500 -9.682007 -10.366536 -9.869545 -11.998150
## [319] -13.911084 -13.280957 -14.343697 -12.989407 -14.804543 -15.387635
## [325] -16.337521 -14.541199 -15.594540 -15.171318 -15.613358 -16.102410
## [331] -17.381459 -19.055516 -19.083737 -17.644803 -16.911221 -17.136940
## [337] -16.102410 -15.444073 -13.976918 -15.284180 -15.801449 -15.538113
## [343] -16.196446 -16.111813 -18.096230 -16.892422 -15.820263 -12.650837
## [349] -12.716664 -10.638203 -11.700951 -12.697853 -12.293450 -13.713574
## [355] -13.826439 -15.124302 -15.622757 -14.212033 -14.635247 -14.437752
## [361] -14.719895 -18.453618 -20.005406 -19.779702 -18.792187 -19.826714
## [367] -18.331345 -17.127533 -19.356465 -21.030526 -19.930169 -20.983517
## [373] -19.027314 -19.140164 -19.347073 -19.158974 -17.983372 -18.726349
## [379] -17.870507 -17.278016 -17.353245 -16.516209 -17.223782 -17.138874
## [385] -16.355835 -17.355862 -16.714333 -17.601159 -17.733239 -18.101170
## [391] -18.006829 -18.450234 -18.035126 -15.667141 -14.185959 -14.752018
## [397] -14.742581 -16.148289 -16.101109 -16.563385 -17.516243 -17.403038
## [403] -16.818112 -17.110581 -17.393601 -16.214322 -15.714306 -14.591629
## [409] -14.742581 -13.402916 -13.921803 -11.931183 -12.242520 -12.657608
## [415] -12.516110 -11.044365 -11.808533 -11.591546 -11.534943 -10.789639
## [421] -8.978268 -9.751873 -11.553814 -11.487770 -9.638665 -10.714158
## [427] -10.044335 -7.138592 -6.091393 -4.572476 -6.091393 -6.006485
## [433] -6.015919 -5.355519 -5.487603 -5.317780 -5.553643 -6.327244
## [439] -6.723469 -6.902741 -8.780144 -11.044365 -11.404000 -9.454396
## [445] -10.864544 -13.126477 -14.318951 -13.921456 -14.176991 -11.640606
## [451] -12.426133 -11.574349 -11.990780 -10.220986 -10.457589 -8.962254
## [457] -9.056900 -8.271374 -7.741379 -7.722454 -10.249382 -9.823491
## [463] -7.230320 -8.157807 -7.712990 -6.842286 -5.072499 -4.523587
## [469] -5.630890 -6.350155 -5.943200 -5.678200 -5.517308 -4.400544
## [475] -5.375351 -3.889481 -3.350026 -4.428933 -6.321759 -6.331231
## [481] -7.315495 -7.154602 -6.520516 -6.406937 -5.820168 -11.735245
## [487] -12.000233 -9.766701 -10.202065 -9.681527 -9.132603 -8.224060
## [493] -6.653012 -7.608883 -9.643670 -9.208321 -7.201928 -6.416409
## [499] -6.794972 -8.214585 -8.517441 -7.050503 -7.097821 -6.785508
## [505] -6.653012 -8.479584 -7.008198 -6.543045 -4.606507 -3.979985
## [511] -2.878800 -2.669964 -2.337716 -2.185833 -1.435887 -1.075169
## [517] -2.252274 -2.185833 -2.062420 -2.783871 -4.748898 -3.666706
## [523] -3.201558 -2.812348 -1.606770 -0.344212 0.529117 2.114421
## [529] 1.848636 1.459415 1.725208 0.718975 1.715725 0.367748
## [535] 1.136653 0.671520 0.453167 -0.220814 -0.116391 -0.078419
## [541] 0.253826 1.241085 1.516384 3.604778 5.009739 4.743938
## [547] 3.823139 4.392711 4.886341 -0.049946 0.348766 -0.239788
## [553] -0.249302 -0.932778 -2.631997 -2.764897 -0.904293 -0.230313
## [559] 0.595562 5.465396 6.633014 4.345234 4.335750 4.335750
## [565] 4.838878 4.686992 4.345234 5.598301 7.003254 7.734195
## [571] 8.816379 8.216930 7.655544 7.979061 8.017116 6.285404
## [577] 5.543239 4.658351 4.239681 4.344348 3.126445 5.600330
## [583] 6.275882 5.714504 4.534656 3.821025 4.858165 5.143611
## [589] 4.648822 5.295841 3.002750 1.775333 1.489872 1.718242
## [595] 0.348087 1.775333 3.269184 5.771602 6.608905 6.085582
## [601] 6.247348 6.466175 6.256847 6.466175 5.847721 6.294902
## [607] 7.484279 7.712650 11.880169 11.861148 9.891552 9.092304
## [613] 4.096973 8.197902 7.798267 6.466175 6.989505 7.779247
## [619] 7.103702 5.381488 5.571788 4.877178 4.943805 5.524211
## [625] 5.809642 7.408161 5.019908 6.294902 6.209270 5.200702
## [631] 3.373828 4.334835 4.154064 2.327190 -0.448750 -1.068791
## [637] -0.429646 -0.839844 -1.774697 -0.668133 -0.734913 -1.269108
## [643] -0.992478 -1.183255 -1.984562 -2.213501 -3.711163 -3.720700
## [649] -3.949639 -4.025959 -3.806557 -2.900319 -2.165802 -1.765156
## [655] -1.402657 -1.097405 -1.364506 -1.078328 -2.661847 -3.281899
## [661] -1.068791 -1.536210 -3.205582 -1.431279 -3.444066 -4.436146
## [667] -4.273980 -6.029206 -5.380532 -6.887742 -8.003834 -7.889367
## [673] -9.301171 -9.749520 -10.712983 -9.911683 -7.498246 -7.107140
## [679] -8.957756 -10.245564 -8.242314 -8.805127 -7.822590 -6.983136
## [685] -8.700200 -9.110386 -9.301171 -7.631798 -9.806755 -11.609677
## [691] -11.895855 -12.191567 -12.725766 -11.914936 -12.716233 -12.725766
## [697] -12.954716 -12.248803 -12.887936 -11.705067 -12.477749 -13.946793
## [703] -13.975529 -14.646050 -16.849171 -14.904671 -13.132599 -12.337555
## [709] -11.475464 -11.140210 -11.810723 -11.398835 -11.542515 -9.981179
## [715] -9.799183 -8.496464 -7.126694 -7.940888 -9.952439 -9.521393
## [721] -10.460114 -10.776211 -12.960186 -12.711132 -12.088513 -12.222615
## [727] -12.845234 -12.002297 -12.931446 -12.538716 -11.954411 -12.251347
## [733] -12.337555 -13.870163 -13.429535 -13.937214 -14.933411 -13.295437
## [739] -15.067517 -13.889317 -13.592385 -12.672818 -18.784085 -18.046517
## [745] -17.615475 -18.257256 -20.182587 -20.584900 -20.115540 -21.609822
## [751] -19.856915 -21.753510 -22.060036 -22.356972 -21.514046 -22.481503
## [757] -21.878037 -20.287949 -18.036950 -17.969586 -19.605351 -18.835583
## [763] -19.489888 -18.931797 -19.085762 -18.922177 -19.874775 -22.193718
## [769] -23.492699 -23.829476 -22.934620 -25.272801 -24.185494 -24.108517
## [775] -23.300251 -23.454213 -20.856228 -22.097489 -23.762124 -23.742875
## [781] -24.705094 -23.531193 -22.530484 -22.732548 -22.636330 -23.290638
## [787] -23.588917 -23.232903 -23.916073 -24.358696 -22.838398 -22.857636
## [793] -21.135273 -20.355885 -19.913258 -19.884396 -19.999859 -20.865857
## [799] -19.403286 -18.412205 -18.008072 -17.709786 -18.200516 -16.227974
## [805] -18.739361 -19.307072 -18.989537 -18.614270 -18.133164 -18.065804
## [811] -17.228680 -17.959958 -17.170948 -18.065804 -18.094670 -19.509129
## [817] -21.125653 -21.087159 -20.990941 -19.970986 -21.953152 -22.020512
## [823] -22.030129 -22.126831 -21.507950 -22.146176 -23.180867 -21.614327
## [829] -22.010796 -21.188843 -20.782704 -23.422615 -23.635361 -23.548325
## [835] -24.186551 -24.815094 -26.217247 -27.155240 -27.764454 -27.870827
## [841] -27.928841 -28.470364 -27.464680 -28.354325 -29.205285 -28.808812
## [847] -27.406666 -26.971512 -27.193924 -28.489705 -28.480034 -29.069909
## [853] -28.895840 -28.093232 -28.944195 -28.199608 -27.571057 -28.238282
## [859] -28.422017 -27.658081 -27.396988 -27.116558 -26.536366 -26.265603
## [865] -25.811112 -26.275273 -26.304284 -27.996529 -27.261612 -26.052861
## [871] -25.559685 -24.573353 -25.569359 -21.614327 -19.825375 -20.405564
## [877] -19.332200 -20.811711 -20.831055 -20.627980 -21.546635 -21.159832
## [883] -21.063134 -21.246861 -21.933434 -22.474957 -20.638089 -20.910218
## [889] -20.871342 -22.095921 -22.669331 -22.853993 -22.154232 -22.387482
## [895] -22.309731 -22.309731 -22.280583 -23.699532 -24.953263 -24.622818
## [901] -24.982422 -24.681137 -25.808533 -25.759930 -25.847401 -26.002903
## [907] -24.156319 -24.496476 -23.835595 -22.922020 -22.912304 -20.958809
## [913] -22.504109 -20.978249 -19.500981 -19.675919 -19.841141 -19.345475
## [919] -20.113274 -20.540898 -19.452393 -18.480500 -19.423230 -17.246209
## [925] -17.022671 -17.178173 -17.285084 -16.692227 -15.817528 -14.592953
## [931] -15.564839 -16.225727 -16.041069 -17.022671 -17.771019 -18.072304
## [937] -17.246209 -17.372551 -16.546448 -17.508618 -17.916802 -18.256966
## [943] -18.295842 -20.725560 -20.997689 -20.288212 -20.191018 -20.336800
## [949] -20.502022 -20.054959 -21.308686 -22.057045 -21.784913 -22.820965
## [955] -23.710411 -24.638943 -24.570527 -24.912617 -24.287075 -23.690857
## [961] -22.732998 -22.039044 -22.908928 -23.309670 -23.104416 -23.163060
## [967] -22.899159 -22.156334 -21.882660 -21.433049 -21.521019 -21.472142
## [973] -21.941296 -22.214970 -22.381134 -22.283390 -22.987130 -22.175881
## [979] -22.254071 -22.009716 -21.755593 -22.078133 -22.400681 -22.664582
## [985] -21.931523 -21.784913 -22.420224 -20.269932 -19.419587 -20.172192
## [991] -20.699997 -21.042084 -21.423272 -20.201512 -19.634621 -20.025578
## [997] -20.015809 -20.054905 -20.905251 -20.690216 -22.742775 -21.911976
## [1003] -21.677403 -22.302945 -21.677403 -22.009716 -22.478875 -22.166108
## [1009] -21.442818 -22.166108 -22.982026 -22.274239 -21.163403 -20.278660
## [1015] -20.386799 -20.504761 -19.964093 -19.767479 -20.445782 -20.052563
## [1021] -20.494931 -19.954262 -20.504761 -20.721028 -21.448483 -21.674580
## [1027] -22.166104 -22.077630 -21.084755 -20.721028 -20.956967 -20.868489
## [1033] -20.337647 -20.534253 -21.694241 -21.291195 -19.905106 -18.695965
## [1039] -19.177658 -19.452904 -19.089180 -18.410889 -17.585133 -16.602089
## [1045] -16.788868 -17.280388 -16.690564 -17.309876 -16.828190 -21.881020
## [1051] -20.553917 -21.045437 -21.979325 -21.782719 -21.930176 -22.480675
## [1057] -21.694241 -22.018643 -21.871190 -22.244744 -21.055264 -21.517292
## [1063] -21.959664 -22.598641 -22.578980 -22.539658 -22.490502 -22.264405
## [1069] -21.645089 -22.392205 -21.949833 -21.674580 -21.232212 -20.809506
## [1075] -20.532711 -20.216370 -21.017106 -21.185162 -22.173726 -21.867272
## [1081] -21.788186 -21.788186 -21.590474 -20.947903 -20.750191 -21.392758
## [1087] -21.679444 -21.610245 -21.382878 -22.163838 -21.481732 -21.807957
## [1093] -22.401093 -21.649784 -21.214817 -21.748642 -22.776753 -22.351670
## [1099] -22.677891 -22.282471 -21.946354 -21.778298 -22.242924 -22.658120
## [1105] -23.488514 -22.816292 -22.727318 -23.389656 -24.131081 -24.506737
## [1111] -25.089989 -24.279366 -25.950039 -26.879288 -27.245060 -26.602494
## [1117] -26.019242 -26.533295 -26.256493 -24.724221 -24.902161 -24.496849
## [1123] -25.307473 -25.327244 -25.406331 -26.513524 -24.921933 -24.645134
## [1129] -25.080105 -25.119645 -25.801758 -24.872506 -23.636799 -23.794972
## [1135] -23.923485 -24.140965 -24.625363 -24.008664 -23.292489 -23.401905
## [1141] -23.541161 -23.551106 -23.541161 -23.730149 -23.262650 -23.909192
## [1147] -23.063713 -22.377381 -23.272595 -22.506691 -21.362805 -22.049138
## [1153] -21.303124 -21.213604 -21.551796 -21.651261 -21.561741 -21.412541
## [1159] -21.163868 -21.482167 -22.496746 -22.238125 -22.188393 -22.884671
## [1165] -22.466900 -23.153237 -23.809727 -24.317013 -24.346856 -24.227490
## [1171] -23.889298 -23.958928 -23.610787 -23.411850 -22.864777 -22.337597
## [1177] -22.407223 -23.073658 -23.948983 -23.322331 -23.083607 -23.690361
## [1183] -22.367436 -22.685734 -23.004033 -22.596211 -21.541848 -23.889298
## [1189] -22.844883 -22.407223 -21.581635 -21.442379 -21.233498 -20.756051
## [1195] -21.024613 -21.153920 -20.646634 -17.165242 -17.772000 -17.006092
## [1201] -16.150666 -14.976941 -14.529332 -14.290612 -14.430611 -13.250611
## [1207] -13.890610 -12.390610 -12.550610 -12.600609 -13.450612 -12.980610
## [1213] -12.830609 -12.800610 -13.380612 -13.570610 -13.720608 -12.880612
## [1219] -12.020611 -12.530610 -12.940609 -12.950612 -13.400608 -12.740609
## [1225] -13.220608 -12.840611 -12.340611 -12.910611 -13.490609 -13.910611
## [1231] -14.550610 -15.350609 -14.850609 -14.410611 -13.860611 -13.550610
## [1237] -13.620610 -13.460610 -12.780610 -12.050610 -13.260609 -13.740609
## [1243] -15.410611 -15.150608 -15.420609 -14.730610 -15.110611 -14.460610
## [1249] -13.800610 -12.810608 -12.700612 -12.380612 -12.100609 -13.320610
## [1255] -13.560608 -12.630612 -12.000611 -11.990609 -10.390610Estrategias de inversión con SWAPS
options(warn = -1)
suppressPackageStartupMessages({
library(tidyverse)
library(lubridate)
})Calcule por medio del modelo de Vasicek la tasas SORF para los próximos 5 años en pagos semestrales. Use información de mercado
# Parámetros del modelo de Vasicek
alpha <- 0.1
b <- 0.03
sigma <- 0.02
r0 <- 0.01
# Simular tasas de interés con el modelo de Vasicek
vasicek_sim <- function(alpha, b, sigma, r0, T, dt) {
n <- T / dt
rates <- numeric(n)
rates[1] <- r0
for (i in 2:n) {
dr <- alpha * (b - rates[i-1]) * dt + sigma * sqrt(dt) * rnorm(1)
rates[i] <- rates[i-1] + dr
}
return(rates)
}
# Simular tasas SORF para 5 años con pagos semestrales
T <- 5
dt <- 0.5
rates <- vasicek_sim(alpha, b, sigma, r0, T, dt)
dates <- seq.Date(Sys.Date(), by = "6 months", length.out = length(rates))
sorf_rates <- data.frame(Date = dates, SORF_Rate = rates)
print(sorf_rates)## Date SORF_Rate
## 1 2024-06-02 0.010000000
## 2 2024-12-02 0.020455400
## 3 2025-06-02 0.046274764
## 4 2025-12-02 -0.003716682
## 5 2026-06-02 0.018470239
## 6 2026-12-02 0.017557822
## 7 2027-06-02 0.019530441
## 8 2027-12-02 0.028475169
## 9 2028-06-02 0.040300453
## 10 2028-12-02 0.053852269Establezca el flujo de pagos de la tasa flotante y la tasa fija
# Contrato SWAP
principal <- 100000000
fixed_rate <- 0.0333
payment_dates <- seq.Date(Sys.Date(), by = "6 months", length.out = length(rates))
# Flujo de pagos de la tasa fija
fixed_payments <- rep(principal * fixed_rate / 2, length(rates))
# Flujo de pagos de la tasa flotante
floating_payments <- principal * sorf_rates$SORF_Rate / 2
payments <- data.frame(Date = payment_dates, Fixed_Payment = fixed_payments, Floating_Payment = floating_payments)
print(payments)## Date Fixed_Payment Floating_Payment
## 1 2024-06-02 1665000 500000.0
## 2 2024-12-02 1665000 1022770.0
## 3 2025-06-02 1665000 2313738.2
## 4 2025-12-02 1665000 -185834.1
## 5 2026-06-02 1665000 923511.9
## 6 2026-12-02 1665000 877891.1
## 7 2027-06-02 1665000 976522.0
## 8 2027-12-02 1665000 1423758.5
## 9 2028-06-02 1665000 2015022.7
## 10 2028-12-02 1665000 2692613.5Valuación de los pagos
discount_rate <- 0.03
# Valor presente de los flujos de pagos
payments <- payments %>%
mutate(
Discount_Factor = exp(-discount_rate * as.numeric(difftime(Date, Sys.Date(), units = "days")) / 365),
PV_Fixed_Payment = Fixed_Payment * Discount_Factor,
PV_Floating_Payment = Floating_Payment * Discount_Factor
)
print(payments)## Date Fixed_Payment Floating_Payment Discount_Factor PV_Fixed_Payment
## 1 2024-06-02 1665000 500000.0 1.0000000 1665000
## 2 2024-12-02 1665000 1022770.0 0.9850715 1640144
## 3 2025-06-02 1665000 2313738.2 0.9704455 1615792
## 4 2025-12-02 1665000 -185834.1 0.9559582 1591670
## 5 2026-06-02 1665000 923511.9 0.9417645 1568038
## 6 2026-12-02 1665000 877891.1 0.9277054 1544629
## 7 2027-06-02 1665000 976522.0 0.9139312 1521695
## 8 2027-12-02 1665000 1423758.5 0.9002875 1498979
## 9 2028-06-02 1665000 2015022.7 0.8868475 1476601
## 10 2028-12-02 1665000 2692613.5 0.8736082 1454558
## PV_Floating_Payment
## 1 500000.0
## 2 1007501.5
## 3 2245356.9
## 4 -177649.6
## 5 869730.8
## 6 814424.3
## 7 892473.9
## 8 1281792.0
## 9 1787017.9
## 10 2352289.2Flujos de diferencia
payments <- payments %>%
mutate(Difference = PV_Floating_Payment - PV_Fixed_Payment)
# Sumar los valores presentes para cada tipo de pago
total_pv_fixed <- sum(payments$PV_Fixed_Payment)
total_pv_floating <- sum(payments$PV_Floating_Payment)
total_difference <- sum(payments$Difference)
# Imprimir resultados
print(payments)## Date Fixed_Payment Floating_Payment Discount_Factor PV_Fixed_Payment
## 1 2024-06-02 1665000 500000.0 1.0000000 1665000
## 2 2024-12-02 1665000 1022770.0 0.9850715 1640144
## 3 2025-06-02 1665000 2313738.2 0.9704455 1615792
## 4 2025-12-02 1665000 -185834.1 0.9559582 1591670
## 5 2026-06-02 1665000 923511.9 0.9417645 1568038
## 6 2026-12-02 1665000 877891.1 0.9277054 1544629
## 7 2027-06-02 1665000 976522.0 0.9139312 1521695
## 8 2027-12-02 1665000 1423758.5 0.9002875 1498979
## 9 2028-06-02 1665000 2015022.7 0.8868475 1476601
## 10 2028-12-02 1665000 2692613.5 0.8736082 1454558
## PV_Floating_Payment Difference
## 1 500000.0 -1165000.0
## 2 1007501.5 -632642.4
## 3 2245356.9 629565.1
## 4 -177649.6 -1769320.0
## 5 869730.8 -698307.2
## 6 814424.3 -730205.2
## 7 892473.9 -629221.5
## 8 1281792.0 -217186.7
## 9 1787017.9 310416.7
## 10 2352289.2 897731.6cat("Valor Presente Total de Pagos Fijos: ", total_pv_fixed, "\n")## Valor Presente Total de Pagos Fijos: 15577107cat("Valor Presente Total de Pagos Flotantes: ", total_pv_floating, "\n")## Valor Presente Total de Pagos Flotantes: 11572937cat("Diferencia Total: ", total_difference, "\n")## Diferencia Total: -4004170# Análisis de la posición
if (total_difference > 0) {
cat("La contraparte que paga la tasa fija obtiene ventaja.\n")
} else {
cat("La contraparte que paga la tasa flotante obtiene ventaja.\n")
}## La contraparte que paga la tasa flotante obtiene ventaja.