BSM_ Assign 1

#Parameters

S0=40
K=40
r=0.08
sigma=0.3
T=91/365

Calculating d1 and d2

d1=log(S0/K)+(r+0.5*sigma^2)*T/(sigma*sqrt(T))
d1

## [1] 0.2080477

d2=d1-sigma*sqrt(T)
d2

## [1] 0.05825337

Calculating Price of a Call

Call_Price=S0*pnorm(d1)-K*exp(-r*T)*pnorm(d2)
Call_Price

## [1] 2.780402

Put_Price=K*exp(-r*T)*pnorm(-d2) - S0*pnorm(-d1)
Put_Price

## [1] 1.990497

Calculating Delta of a Call

delta=pnorm(d1)
delta

## [1] 0.5824042

Calculating Gamma of a Call

gamma=dnorm(d1)/(S0*sqrt(T)*sigma)
gamma

## [1] 0.06515618

Calculating Rho of a Call

rho=T*K*exp(-r*T)*pnorm(d2)
rho

## [1] 5.114889

Calculating Vega of a Call

Vega=dnorm(d1)*S0*sqrt(T)
Vega

## [1] 7.79732

Calculating theta of a Call

theta1=-r*K*exp(-r*T)*pnorm(d2)
theta2=dnorm(d1)*sigma*S0*sqrt(T)
theta3=2*sqrt(T)
theta=theta1-theta2/theta3
theta

## [1] -3.983668

myresult<-data.frame("price"=Call_Price, "delta"=delta, "gamma"=gamma,"Vega"=Vega, "rho"=rho, "theta"=theta)
myresult

##      price     delta      gamma    Vega      rho     theta
## 1 2.780402 0.5824042 0.06515618 7.79732 5.114889 -3.983668

References