Modify given R code or create your own R code using Montecarlo to solve this problem.

Consider a call option with S0 = 50, K = 51 , r=.05 , =.3 and T=.5 . Use the Monte Carlo estimation of stock price to estimate Delta, Gamma and vega for the standard call option.

```{r} r=.05 sigma=.3 TT=.5 SO=50 dS=.0001 K=51 delta=exp(-r*TT)*(pnorm((log(SO/K)+TT*(r+sigma^2/2))/(sigma*sqrt(TT)))-1) delta ST=SO*exp((r-sigma^2/2)*TT+sigma*sqrt(TT)*rnorm(10000))

payoff=(K-ST)*(K-ST>0)

f2= exp(-r*TT)*mean(payoff)

SO=SO+.01

ST=SO*exp((r-sigma^2/2)*TT+sigma*sqrt(TT)*rnorm(10000)) payoff=(K-ST)*(K-ST>0) f1=exp(-r*TT)*mean(payoff) f2-f1 (f2-f1)/(-dS)

```