HW3 Q1 b 10^4

# Pricing call option using Monte-Carlo Method

#Package Utilised
library(MASS)

# Given parameters
S0 = 100;         # Initial Stock Price
m = 10;           # Number of stocks with dynamics under the risk neutral measure
K = 100*m;        # Strike Price
r = 0.04;         # Risk free rate
sig = 0.15;       # Standard deviation
T = 1;
p = 0.2;          # Correlation
N = 10000;       # Number of simulations

# Covariance Matrix
SIG   = diag(rep(1-p,10)) + matrix(p,10,10);

# Monte Carlo simulation
W         <- mvrnorm(n = N, rep(0,10), SIG);
SP        <- (S0 * exp((r - (sig**2)/2)*T + (sig*W)));
P_est <- rowSums(SP)
P     <- exp(-r*T)*pmax(P_est - K, 0);

C_mc <- mean(P)
C_mc