GMB VAR MonteCarlo - Practica Calificada 2
Eduardo Falcon Shareva
18/6/2020
pkges<-c("pdfetch","tseries","tidyverse","forecast")
#install.packages(pkges)
lapply(pkges,"library",character.only=T)## Warning: package 'pdfetch' was built under R version 3.6.3## Warning: package 'tseries' was built under R version 3.6.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Warning: package 'tidyverse' was built under R version 3.6.3## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.1 v purrr 0.3.4
## v tibble 3.0.1 v dplyr 0.8.5
## v tidyr 1.1.0 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.5.0## Warning: package 'tibble' was built under R version 3.6.3## Warning: package 'tidyr' was built under R version 3.6.3## Warning: package 'readr' was built under R version 3.6.3## Warning: package 'purrr' was built under R version 3.6.3## Warning: package 'dplyr' was built under R version 3.6.3## Warning: package 'stringr' was built under R version 3.6.3## Warning: package 'forcats' was built under R version 3.6.3## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()## Warning: package 'forecast' was built under R version 3.6.3## [[1]]
## [1] "pdfetch" "stats" "graphics" "grDevices" "utils" "datasets"
## [7] "methods" "base"
##
## [[2]]
## [1] "tseries" "pdfetch" "stats" "graphics" "grDevices" "utils"
## [7] "datasets" "methods" "base"
##
## [[3]]
## [1] "forcats" "stringr" "dplyr" "purrr" "readr" "tidyr"
## [7] "tibble" "ggplot2" "tidyverse" "tseries" "pdfetch" "stats"
## [13] "graphics" "grDevices" "utils" "datasets" "methods" "base"
##
## [[4]]
## [1] "forecast" "forcats" "stringr" "dplyr" "purrr" "readr"
## [7] "tidyr" "tibble" "ggplot2" "tidyverse" "tseries" "pdfetch"
## [13] "stats" "graphics" "grDevices" "utils" "datasets" "methods"
## [19] "base"#DATOS DE EXAS Exact SCIENCE
EXASdata <- pdfetch_YAHOO("EXAS",from = as.Date("2019-01-01"),to = as.Date("2020-01-01"), interval = '1d')#USANDO LA FUNCION SUMMARY PARA OBTERNER LA SERIE DE DATOS ESTADISTICOS
summary(EXASdata)## Index EXAS.open EXAS.high EXAS.low
## Min. :2019-01-02 Min. : 61.88 Min. : 64.43 Min. : 60.95
## 1st Qu.:2019-04-02 1st Qu.: 87.55 1st Qu.: 89.57 1st Qu.: 85.92
## Median :2019-07-02 Median : 93.88 Median : 95.93 Median : 91.66
## Mean :2019-07-02 Mean : 97.02 Mean : 98.80 Mean : 95.10
## 3rd Qu.:2019-10-01 3rd Qu.:109.75 3rd Qu.:111.81 3rd Qu.:107.50
## Max. :2019-12-31 Max. :122.83 Max. :123.99 Max. :120.40
## EXAS.close EXAS.adjclose EXAS.volume
## Min. : 61.98 Min. : 61.98 Min. : 355400
## 1st Qu.: 87.83 1st Qu.: 87.83 1st Qu.: 1201825
## Median : 93.83 Median : 93.83 Median : 1562900
## Mean : 97.06 Mean : 97.06 Mean : 1838430
## 3rd Qu.:108.81 3rd Qu.:108.81 3rd Qu.: 2090625
## Max. :122.49 Max. :122.49 Max. :14692800#UTILIZAREMOS LOS PRECIOS AJUSTADOS COREESPONDIENTES A LA QUINTA COLUMNA (CIERRE) TAMBIEN UTILIZAREMOS LA FUNCION HEAD, TAIL PARA OBTENER EL PRIMER Y ULTIMO DATO PARA LUEGO OBTENER NUESTRA SERIE DE TIEMPO
EXAS <- EXASdata[,5]
head(EXAS,1)## EXAS.adjclose
## 2019-01-02 64.14tail(EXAS,1)## EXAS.adjclose
## 2019-12-31 92.48#CREANDO NUESTRA SERIE DE TIEMPO
ts.EXAS <- ts(EXAS, start = c(2019,1), frequency = 365)
summary(ts.EXAS)## EXAS.adjclose
## Min. : 61.98
## 1st Qu.: 87.83
## Median : 93.83
## Mean : 97.06
## 3rd Qu.:108.81
## Max. :122.49#LUEGO HALLAREMOS LOS RETORNOS DISCRETOS Y CONTINUOS RESPECTIVAMENTE
tprecios <- length(ts.EXAS)
ret.dis <- numeric(length = tprecios)
for (i in 2:tprecios) {
ret.dis[i] <- (ts.EXAS[i]/ts.EXAS[i - 1]) - 1
}
ts.plot(ret.dis)
#RETORNOS CONTINUOS
ret.con<-diff(log(ts.EXAS))
ts.plot(ret.con)
#MOVIMIENTO BROWNIANO GEOMETRICO
NUM DE SIMULACIONES: 10000
UTILIZAREMOS EL PRECIO INICIAL
t<-365
tseq <- 1:t
dt <- 1/t
mu<-mean(ret.con)
s<-sd(ret.con)
P0<-64.14
nsim<-10000
m <- matrix(ncol = nsim, nrow = t)
for (i in 1:nsim) {
m[1,i] <- P0
for (h in 2:t) {
e <- rnorm(1)
m[h, i]<- m[(h-1),i]*exp((mu-(s^2)/2)*dt+s*e*sqrt(dt))
}
}#GRAFICA DE LAS SIMULACIONES DE GBM
gbm_df <- as.data.frame(m) %>%
mutate(ix = 1:nrow(m)) %>%
pivot_longer(-ix, names_to = 'sim', values_to = 'price')
gbm_df %>%
ggplot(aes(x=ix, y=price, color=sim)) +
geom_line() +
theme(legend.position = 'none')
#VAR MONTECARLO -> alpha: 0.01
t<-365
tseq <- 1:t
dt <- 1/t
mu<-mean(ret.con)
s<-sd(ret.con)
P0<-64.14
nsim<-10000
m1 <- matrix(ncol = nsim, nrow = t)
for (i in 1:nsim) {
m1[1,i] <- P0
for (h in 2:t) {
e1 <- rnorm(1)
m1[h, i]<- m1[(h-1),i]*exp((mu-(s^2)/2)*dt+s*e1*sqrt(dt))
}
}gbm_df1 <- as.data.frame(m1) %>%
mutate(ix = 1:nrow(m1)) %>%
pivot_longer(-ix, names_to = 'sim', values_to = 'Precio')
gbm_df1 %>%
ggplot(aes(x=ix, y=Precio, color=sim)) +
geom_line() +
theme(legend.position = 'none')
VAR_99 <- numeric(length = nsim)
for(i in 1:nsim){
sim.ts <- m1[, i]
sim.R <- diff(log(sim.ts))
sim.q <- quantile(sim.R, 0.01, na.rm = TRUE)
sim.var <- exp(sim.q) - 1
VAR_99[i]<- sim.var
}plot (density (VAR_99), main = "VaR 99%")
quantile(VAR_99,0.025)## 2.5%
## -0.003947643quantile(VAR_99,0.975)## 97.5%
## -0.002888132mean(VAR_99)## [1] -0.003384331sd(VAR_99)## [1] 0.0002673521mean_mon_99<-c(mean(VAR_99)*100000)
sd_mon_99<-c(sd(VAR_99)*100000)
quantile_mon_99_1<-quantile(VAR_99,0.025)*100000
quantile_mon_99_2<-quantile(VAR_99,0.975)*100000mean_mon_99## [1] -338.4331sd_mon_99## [1] 26.73521quantile_mon_99_1## 2.5%
## -394.7643quantile_mon_99_2## 97.5%
## -288.8132#LA PERDIDA MEDIA ESPERADA AL 99% DE CONFIANZA ES 393.82
####VAR MONTECARLO -> alpha: 0.05
t<-365
tseq <- 1:t
dt <- 1/t
mu<-mean(ret.con)
s<-sd(ret.con)
P0<-64.14
nsim<-10000
m2 <- matrix(ncol = nsim, nrow = t)
for (i in 1:nsim) {
m2[1,i] <- P0
for (h in 2:t) {
e2 <- rnorm(1)
m2[h, i]<- m2[(h-1),i]*exp((mu-(s^2)/2)*dt+s*e2*sqrt(dt))
}
}gbm_df2 <- as.data.frame(m2) %>%
mutate(ix = 1:nrow(m2)) %>%
pivot_longer(-ix, names_to = 'sim', values_to = 'Precio')
gbm_df2 %>%
ggplot(aes(x=ix, y=Precio, color=sim)) +
geom_line() +
theme(legend.position = 'none')
VAR_95 <- numeric(length = nsim)
for(i in 1:nsim){
sim.ts <- m2[, i]
sim.R <- diff(log(sim.ts))
sim.q <- quantile(sim.R, 0.05, na.rm = TRUE)
sim.var <- exp(sim.q) - 1
VAR_95[i] <- sim.var
}plot (density (VAR_95), main = "VaR 95%")
#OBTENIENDO LOS QUANTILES, MEDIA, DES. ESTANDAR
quantile(VAR_95,0.025)## 2.5%
## -0.002748879quantile(VAR_95,0.975)## 97.5%
## -0.002120617mean(VAR_95)## [1] -0.002428639sd(VAR_95)## [1] 0.0001599658mean_mon_95<-c(mean(VAR_99)*100000)
sd_mon_95<-c(sd(VAR_99)*100000)
quantile_mon_95_1<-quantile(VAR_95,0.025)*100000
quantile_mon_95_2<-quantile(VAR_95,0.975)*100000#VAR MONTECARLO -> alpha: 0.1
t<-365
tseq <- 1:t
dt <- 1/t
mu<-mean(ret.con)
s<-sd(ret.con)
P0<-64.14
nsim<-10000
m3 <- matrix(ncol = nsim, nrow = t)
for (i in 1:nsim) {
m3[1,i] <- P0
for (h in 2:t) {
e3 <- rnorm(1)
m3[h, i]<- m3[(h-1),i]*exp((mu-(s^2)/2)*dt+s*e3*sqrt(dt))
}
}gbm_df3 <- as.data.frame(m3) %>%
mutate(ix = 1:nrow(m3)) %>%
pivot_longer(-ix, names_to = 'sim', values_to = 'Precio')
gbm_df3 %>%
ggplot(aes(x=ix, y=Precio, color=sim)) +
geom_line() +
theme(legend.position = 'none')
VAR_90 <- numeric(length = nsim)
for(i in 1:nsim){
sim.ts <- m3[, i]
sim.R <- diff(log(sim.ts))
sim.q <- quantile(sim.R, 0.1, na.rm = TRUE)
sim.var <- exp(sim.q) - 1
VAR_90[i] <- sim.var
}plot (density (VAR_90), main = "VaR 90%")