double SimpleMonteCarlo3(const VanillaOption& TheOption,
double Spot,
double Vol,
double r,
unsigned long NumberOfPaths)
{
double Expiry = TheOption.GetExpiry();
double variance = Vol*Vol*Expiry;
double rootVariance = sqrt(variance);
double itoCorrection = -0.5*variance;
double movedSpot = Spot*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 = TheOption.OptionPayoff(thisSpot);
runningSum += thisPayoff;
}
double mean = runningSum / NumberOfPaths;
mean *= exp(-r * Expiry);
return mean;
}
double MilsteinScheme1(double start,double strike, double t,int NofIntervals,double r, double d,double sigma,double (*pt2func1)(double,double,double), double (*pt2func2)(double,double),double (*pt2func3)(double) ){
double dt=t/NofIntervals;
double x=start;
for (int i=0;i<NofIntervals;i++){
double a=pt2func1(x,r,d);
double b=pt2func2(x,sigma);
double c=pt2func3(sigma);
double dw=GetOneGaussianByBoxMuller()*sqrt(dt);
x+=a*dt+b*dw+0.5*b*c*(dw*dw-dt);
}
double thisPayoff = x - strike;
thisPayoff = thisPayoff >0 ? thisPayoff : 0;
return thisPayoff*exp(-r*t);
}
