Basket Call Option via C++

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Two stocks, with correlation rho, European type, payoff is Max(S1-S2, 0). First, Box-Muller algorithm,

#ifndef BM_GAUSSIAN_HPP_INCLUDED#define BM_GAUSSIAN_HPP_INCLUDED#include <cstdlib>#include <cmath>#include <vector>double uniformRandom(){  return (double)(rand()+1.0)/(double)(RAND_MAX+1.0);}void normalRandom(std::vector<double>& v){  double u1=uniformRandom();  double u2=uniformRandom();  v[0] = cos(8.0*atan(1.0)*u2)*sqrt(-2.0*log(u1));  v[1] = sin(8.0*atan(1.0)*u1)*sqrt(-2.0*log(u2));}#endif // BM_GAUSSIAN_HPP_INCLUDED

main function

#include <iostream>#include <cstdlib>#include <cmath>#include <vector>#include <./BM_Gaussian.hpp>using namespace std;int main(){    // set option contract parameters;    double T = 1.0;    double r = 0.01;    // stock parameters;    double S_10 = 100;    double sigma_1  = 0.1;    double S_20 = 105;    double sigma_2  = 0.05;    double rho = -0.8;    // monte carlo parameters    int npaths = 100000;    int nsteps = 100;    double S1, S2, r1, r2;    vector<double> rnorm(2);    double sumpayoff = 0.0;    double dt = double(T)/double(nsteps);    for (int i=0; i<npaths; i++){        S1 = S_10;        S2 = S_20;        for (int j=0; j<nsteps; j++){            normalRandom(rnorm);            r1 = rnorm[0];            r2 = rnorm[0]*rho + rnorm[1]*sqrt(1-rho*rho);            S1 *= exp((r-0.5*sigma_1*sigma_1)*dt + sigma_1*sqrt(dt)*r1);            S2 *= exp((r-0.5*sigma_2*sigma_2)*dt + sigma_2*sqrt(dt)*r2);        }        sumpayoff += max(r1-r2, 0.0);    }    double callprice = double(sumpayoff)/double(npaths);    cout << "Call Price: " << callprice << endl;    return 0;}

Correlation will affect the call price. To the extreme, if rho=1, stocks move together, the gap could be small, call price will be low. Negative rho generates high call price.

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