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));
}
}
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;
}
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;
}
// 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;
}