Files

BlackScholesModel.cpp

#include "BlackScholesModel.h"

using namespace std;

#include "matlib.h"

BlackScholesModel::BlackScholesModel() :
    drift(0.0),
    stockPrice(0.0),
    volatility(0.0),
    riskFreeRate(0.0),
    date(0.0) {
}

/**
 *  Creates a price path according to the model parameters
 */
vector<double> BlackScholesModel::
            generateRiskNeutralPricePath(
        double toDate,
        int nSteps ) const {
    return generatePricePath( toDate, nSteps, riskFreeRate );
}

/**
 *  Creates a price path according to the model parameters
 */
vector<double> BlackScholesModel::generatePricePath(
        double toDate,
        int nSteps ) const {
    return generatePricePath( toDate, nSteps, drift );
}


/**
 *  Creates a price path according to the model parameters
 */
vector<double> BlackScholesModel::generatePricePath(
        double toDate,
        int nSteps,
        double drift ) const {
    vector<double> path(nSteps,0.0);
    vector<double> epsilon = randn( nSteps );
    double dt = (toDate-date)/nSteps;
    double a = (drift - volatility*volatility*0.5)*dt;
    double b = volatility*sqrt(dt);
    double currentLogS = log( stockPrice );
    for (int i=0; i<nSteps; i++) {
        double dLogS = a + b*epsilon[i];
        double logS = currentLogS + dLogS;
        path[i] = exp( logS );
        currentLogS = logS;
    }
    return path;
}

////////////////////////////////
//
//   TESTS
//
////////////////////////////////

void testRiskNeutralPricePath() {
    rng("default");

    BlackScholesModel bsm;
    bsm.riskFreeRate = 0.05;
    bsm.volatility = 0.1;
    bsm.stockPrice = 100.0;
    bsm.date = 2.0;

    int nPaths = 10000;
    int nsteps = 5;
    double maturity = 4.0;
    vector<double> finalPrices(nPaths,0.0);
    for (int i=0; i<nPaths; i++) {
        vector<double> path =
            bsm.generateRiskNeutralPricePath( maturity,
                                              nsteps );
        finalPrices[i] = path.back();
    }
    ASSERT_APPROX_EQUAL( mean( finalPrices ),
        exp( bsm.riskFreeRate*2.0)*bsm.stockPrice, 0.5);
}

void testVisually() {
    BlackScholesModel bsm;
    bsm.riskFreeRate = 0.05;
    bsm.volatility = 0.1;
    bsm.stockPrice = 100.0;
    bsm.date = 2.0;

    int nSteps = 1000;
    double maturity = 4.0;

    vector<double> path = bsm.generatePricePath( maturity,
                                                 nSteps );
    double dt = (maturity-bsm.date)/nSteps;
    vector<double> times = linspace(dt, maturity, nSteps );
    plot("examplePricePath.html",
         times,
         path );
}


void testBlackScholesModel() {
    TEST( testRiskNeutralPricePath );
    TEST( testVisually );
}