MC simulation of Black Scholes in R

stock=398.79

sigma=0.32

strike=300

TTM=2.5

rf=0.01

num.sim<-100000

R<-(rf-0.5*sigma^2)*TTM

R

SD<-sigma*sqrt(TTM)

SD

TTM.price<-stock*exp(R+SD*rnorm(num.sim,0,1))

TTM.call<-pmax(0,TTM.price-strike)

PV.call<-TTM.call*(exp(-rf*TTM))

mean(PV.call)

TTM.put<-pmax(0,strike-TTM.price)

PV.put<-TTM.put*(exp(-rf*TTM))

mean(PV.put)

#Let's calculate Black-Scholes value fr call and put option#

d1<-(log(stock/strike)+(rf+0.5*sigma^2)*TTM)/(sigma*sqrt(TTM))

d2<-d1-(sigma*sqrt(TTM))

BS.call<-stock*pnorm(d1,mean=0,sd=1)-strike*exp(-rf*TTM)*pnorm(d2,mean=0,sd=1)

BS.call

BS.put<-BS.call-stock+strike*exp(-rf*TTM)

BS.put

 #”ctrl+shft+enter” to process#