Answer Happy

using Montecarlo create an R code to solve problem
Consider a call option with S0=50),\(K=51 , r=.05 , σ=.3 and
T=.5 . Use the Monte Carlo estimation of stock price to estimate
Delta, Gamma and vega for the standard call option and compare it
with the formulas given in the book.
The following is given code just modify it
```{r}
ST=50*exp((.05-.3^2/2)*.5+.3*sqrt(.5)*rnorm(10))
payoff=(51-ST)*(51-ST>0)
ST
payoff
exp(-.05*.5)*mean(payoff)
ST=50*exp((.05-.3^2/2)*.5+.3*sqrt(.5)*rnorm(10000))
payoff=(51-ST)*(51-ST>0)
exp(-.05*.5)*mean(payoff)
```