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 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));
}
}
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;
}
// Copies the member data
void VanillaOption::copy(const VanillaOption& rhs)
{
K = rhs.getK();
r = rhs.getr();
T = rhs.getT();
S = rhs.getS();
sigma = rhs.getsigma();
}
//copies the member data
void VanillaOption::copy(const VanillaOption& rhs)
{
k = rhs.get_k();
T = rhs.get_T();
r = rhs.get_r();
S = rhs.get_S();
sigma = rhs.get_sigma();
}
const FUNCTIONSDLL_API double simpleMonteCarlo(
const VanillaOption& vanillaOption,
const double spot, const Parameters& volatility,
const Parameters& interestRate, const size_t numberOfPath,
Statistics& gatherer)
{
const double maturity = vanillaOption.getMaturity();
const int seed = 100;
boost::random::mt19937 gen(seed);
boost::random::uniform_01<> dist;
boost::random::variate_generator<boost::random::mt19937&, boost::random::uniform_01<> > rand(gen, dist);
const size_t numberOfSteps = 100;
const double dt = maturity / numberOfSteps;
boost::accumulators::accumulator_set<double, boost::accumulators::stats<boost::accumulators::tag::mean> > accumulator;
const double variance = volatility.IntegralSquare(0.0, maturity);
const double rootVariance = std::sqrt(variance);
const double itoCorrection = -0.5 * variance;
const double movedSpot = spot * std::exp(interestRate.Integral(0.0, maturity) + itoCorrection);
double thisSpot = 0.0;
const double discountFactor = std::exp(-interestRate.Integral(0.0, maturity));
// create paths
for (size_t i = 0; i < numberOfPath; ++i)
{
// by one step
const double randomness = rand();
thisSpot = movedSpot * std::exp(rootVariance * randomness);
double thisPayoff = vanillaOption.getPayoff(thisSpot);
//double nextSpot = spot;
//for (size_t step = 0; step < numberOfSteps; ++step)
//{
// nextSpot += nextSpot * (interestRate * dt - 0.5 * volatility * volatility * std::sqrt(dt) * dist(generator));
//}
gatherer.dumpOneResult(thisPayoff * discountFactor);
accumulator(thisPayoff);
}
// assume interestRate is fixed.
const double price = boost::accumulators::mean(accumulator) * discountFactor;
return price;
}
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;
}