void SimpleMonteCarloForLRDelta(const VanillaOption& TheOption, double Spot, const Parameters& Vol, const Parameters& r, unsigned long NumberOfPaths, StatisticsMC& gatherer, RandomBase& generator) { generator.ResetDimensionality(1); double Expiry = TheOption.GetExpiry(); double variance = Vol.IntegralSquare(0,Expiry); // sigma^2T double rootVariance = sqrt(variance); double itoCorrection = -0.5*variance; double movedSpot = Spot*exp(r.Integral(0,Expiry) +itoCorrection); double averageR = r.Integral(0,Expiry); double subtractNumerator = averageR + itoCorrection; double thisSpot; double discounting = exp(-r.Integral(0,Expiry)); MJArray VariateArray(1); for (unsigned long i=0; i < NumberOfPaths; i++) { generator.GetGaussians(VariateArray); thisSpot = movedSpot*exp( rootVariance*VariateArray[0]); double thisPayOff = (TheOption.OptionPayOff(thisSpot))*(log(thisSpot/Spot) - subtractNumerator)/(Spot*variance); gatherer.DumpOneResult(thisPayOff*discounting); // payoff*Psi/Phi see (p. 195 of JoshiConcepts) } return; }
void SimpleMonteCarlo6(const VanillaOption& TheOption, double Spot, const Parameters& Vol, const Parameters& r, unsigned long NumberOfPaths, StatisticsMC& gatherer, RandomBase& generator) { generator.ResetDimensionality(1); double Expiry = TheOption.GetExpiry(); double variance = Vol.IntegralSquare(0,Expiry); double rootVariance = sqrt(variance); double itoCorrection = -0.5*variance; double movedSpot = Spot*exp(r.Integral(0,Expiry) +itoCorrection); double thisSpot; double discounting = exp(-r.Integral(0,Expiry)); MJArray VariateArray(1); for (unsigned long i=0; i < NumberOfPaths; i++) { generator.GetGaussians(VariateArray); thisSpot = movedSpot*exp( rootVariance*VariateArray[0]); double thisPayOff = TheOption.OptionPayOff(thisSpot); gatherer.DumpOneResult(thisPayOff*discounting); } return; }
void SimpleMonteCarlo_tol(const VanillaOption& TheOption, double Spot, const Parameters& Vol, const Parameters& r, double tol, double maxLoops, StatisticsMC& gatherer, RandomBase& generator, double target) { generator.ResetDimensionality(1); double Expiry = TheOption.GetExpiry(); double variance = Vol.IntegralSquare(0,Expiry); double rootVariance = sqrt(variance); double itoCorrection = -0.5*variance; double movedSpot = Spot*exp(r.Integral(0,Expiry) +itoCorrection); double thisSpot; double discounting = exp(-r.Integral(0,Expiry)); MJArray VariateArray(1); double error = 100.0; double loops = 0.0; double running_sum = 0.0; double prev_res = 0.0; while( (abs(error) > tol) && (loops < maxLoops)) { generator.GetGaussians(VariateArray); thisSpot = movedSpot*exp( rootVariance*VariateArray[0]); double thisPayOff = TheOption.OptionPayOff(thisSpot); gatherer.DumpOneResult(thisPayOff*discounting); if(loops > 0){ prev_res = running_sum/loops; running_sum += thisPayOff*discounting; loops++; error = abs(target - running_sum/loops); } else{ running_sum += thisPayOff*discounting; loops++; } } return; }
void SimpleMonteCarlo( const VanillaOption& theOption, double Spot, Parameters Vol, Parameters r, unsigned long NumberOfPaths, StatisticsMC& gatherer, RandomBase& generator) { double Expiry = theOption.GetExpiry(); double variance = Vol.IntegralSquare(0, Expiry); double rootVariance = sqrt(variance); double itoCorrection = -0.5 * variance; double movedSpot = Spot * exp(r.Integral(0, Expiry) + itoCorrection); double thisSpot; double discounting = exp(-r.Integral(0, Expiry)); std::vector<double> VariateVector(1); for (unsigned long i = 0; i < NumberOfPaths; i++) { generator.GetGaussian(VariateVector); thisSpot = movedSpot * exp(rootVariance * VariateVector[0]); gatherer.DumpOneResult(discounting * theOption.OptionPayOff(thisSpot)); } }
// Project 1 - Euler Stepping void SimpleMonteCarlo7(const VanillaOption& TheOption, double Spot, const Parameters& Vol, const Parameters& r, unsigned long NumberOfPaths, unsigned long NumberOfSteps, StatisticsMC& gatherer, RandomBase& generator) { //generator.ResetDimensionality(1); generator.ResetDimensionality(NumberOfSteps); double Expiry = TheOption.GetExpiry(); double deltaT = Expiry/NumberOfSteps; double variance = Vol.IntegralSquare(0,Expiry); // \sigma^2T double rootVariance = sqrt(variance/ NumberOfSteps); // \sigma \sqrt{Delta T} double rDeltaT= (r.Integral(0,Expiry)/Expiry)*deltaT; // this assumes r is constant. //double itoCorrection = -0.5*variance; // -\sigma^2 T/2 //double movedSpot = Spot*exp(r.Integral(0,Expiry) +itoCorrection); double thisSpot= Spot; double discounting = exp(-r.Integral(0,Expiry)); MJArray VariateArray(NumberOfSteps); double nextSpot=0.0; for (unsigned long i=0; i < NumberOfPaths; i++) { // I guess this method fills the MJArray with Gaussians generator.GetGaussians(VariateArray); thisSpot=Spot; //reset starting point for each path. for (unsigned long j= 0; j < NumberOfSteps; j++) { nextSpot = thisSpot*(1 + rDeltaT + rootVariance*(VariateArray[j])); thisSpot=nextSpot; } double thisPayOff = TheOption.OptionPayOff(nextSpot); gatherer.DumpOneResult(thisPayOff*discounting); } return; }
void SimpleStepping_tol(const VanillaOption& TheOption, double Spot, const Parameters& Vol, const Parameters& r, double tol, double maxLoops, int numSteps, StatisticsMC& gatherer, RandomBase& generator, double target) { generator.ResetDimensionality(numSteps); double Expiry = TheOption.GetExpiry(); double variance = Vol.IntegralSquare(0,Expiry)/Expiry; double rootVariance = sqrt(variance); double rr = r.Integral(0,Expiry)/Expiry; double discounting = exp(-r.Integral(0,Expiry)); MJArray VariateArray(numSteps); double error = 100.0; double loops = 0.0; double running_sum = 0.0; double prev_res = 0.0; while( (abs(error) > tol) && (loops < maxLoops)) { generator.GetGaussians(VariateArray); //Very similar to simple MC but generates thisSpot by stepping double thisSpot = GeneratePath(r, Spot, Vol, Expiry, numSteps, generator); double thisPayOff = TheOption.OptionPayOff(thisSpot); gatherer.DumpOneResult(thisPayOff*discounting); if(loops > 0){ prev_res = running_sum/loops; running_sum += thisPayOff*discounting; loops++; error = abs(target - running_sum/loops); } else{ running_sum += thisPayOff*discounting; loops++; } } return; }