compare MC and BS

europeanCallOption.cpp

#include <iostream>
#include <cmath>
#include "UTRandom1.h"
#include "UTNormals.h"

using namespace std;

double SimpleMonteCarlo1(double Expiry,
	double Strike,
	double Spot,
	double Vol,
	double r,
	unsigned long NumberOfPaths)
{

	double variance = Vol*Vol*Expiry;
	double rootVariance = sqrt(variance);
	double itoCorrection = -0.5*variance;

	double movedSpot = Spot*std::exp(r*Expiry + itoCorrection);
	double thisSpot;
	double runningSum = 0;

	for (unsigned long i = 0; i < NumberOfPaths; i++)
	{
		double thisGaussian = GetOneGaussianByBoxMuller();
		thisSpot = movedSpot*exp(rootVariance*thisGaussian);
		double thisPayoff = thisSpot - Strike;
		thisPayoff = thisPayoff >0 ? thisPayoff : 0;
		runningSum += thisPayoff;
	}

	double mean = runningSum / NumberOfPaths;
	mean *= exp(-r*Expiry);
	return mean;
}

double blackSholesCall(double Expiry,
                         double Strike,
                         double Spot,
                         double Vol,
                         double r)
{
    double d1=(log(Spot/Strike) + (r+Vol*Vol/2.)*(Expiry))/(Vol*sqrt(Expiry));
    double d2=(log(Spot/Strike) + (r-Vol*Vol/2.)*(Expiry))/(Vol*sqrt(Expiry));
    return CumulativeNormal(d1)*Spot - CumulativeNormal(d2)*Strike*exp(-r*(Expiry));
}

int main()
{
    
    double Expiry;
	double Strike;
	double Spot;
	double Vol;
	double r;
	unsigned long NumberOfPaths;

	cout << "\nEnter expiry\n";
	cin >> Expiry;

	cout << "\nEnter strike\n";
	cin >> Strike;

	cout << "\nEnter spot\n";
	cin >> Spot;

	cout << "\nEnter vol\n";
	cin >> Vol;

	cout << "\nr\n";
	cin >> r;

	cout << "\nNumber of paths\n";
	cin >> NumberOfPaths;

	double mc = SimpleMonteCarlo1(Expiry,
		Strike,
		Spot,
		Vol,
		r,
		NumberOfPaths);
    
    double ana = blackSholesCall(Expiry,
        Strike,
        Spot,
        Vol,
        r);
    
    cout << "Monte Carlo: " << mc << "\n";
    cout << "Analytic: " << ana << "\n";
    
	double tmp;
	cin >> tmp;

	return 0;
}


/* Output

Enter expiry
2

Enter strike
14000

Enter spot
14500

Enter vol
0.38

r
0.06

Number of paths
10000

Monte Carlo: 4055.57
Analytic: 4007.4

done

Program ended with exit code: 0

*/