/// <summary>
/// override the <method>DipathByAntitheticMethod</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point
/// </summary>
public double[][] DipathByAntitheticMethod(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps, bool visualizationFlag = false, Form1 form = null)
{
double[][] pricePath = new double[2][];
pricePath[0] = new double[timeSteps + 1];
pricePath[1] = new double[timeSteps + 1];
StochasticAssetPrice S2 = new StochasticAssetPrice(S);
double dt = totalTime / (double)timeSteps;
pricePath[0][0] = S.CurrentPrice;
pricePath[1][0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
double z2 = -z;
pricePath[0][i] = GetNextPrice(S, dt, z);
pricePath[1][i] = GetNextPrice(S2, dt, z2);
}
if (visualizationFlag & form != null)
{
double[] X = new double[timeSteps + 1];
for (int i = 0; i <= timeSteps; i++)
{
X[i] = i;
}
form.add(X, pricePath[0], "");
form.add(X, pricePath[1], "");
}
return(pricePath);
}
/// <summary>
/// override the <method>GeneratingRandomPricePath</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point.
/// </summary>
public double[] GeneratingRandomPricePath(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps)
{
double[] pricePath = new double[timeSteps + 1];
double dt = totalTime / (double)timeSteps;
pricePath[0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
pricePath[i] = GetNextPrice(S, dt, z);
}
return(pricePath);
}
/// <summary>
/// override the <method>PricingByMCSim</method>
/// In each scenario, a price path is generated and the option value under
/// this scenario is only decided by the final price. So, we take the average
/// for the 'value at maturity' of all the simulated scenarios and
/// discounted as the approximation for the option value.
/// This method also outputs the standard error for the approximation.
/// </summary>
public override double[] PricingByMCSim(StochasticAssetPrice S, IDiscretizationScheme D, int numOfScenarios,
int timeSteps, bool antitheticFlag)
{
double[] Result = new double[2]; //record the approximated price and standard error
double[] Sample = new double[numOfScenarios]; //record value at maturity for each scenario
double sumValue = 0.0; //record cumulative sum of Sample array
GaussianGenerator nrand = new GaussianGenerator();
if (antitheticFlag)
{
//when antithetic variance reduction technique is used
for (int i = 0; i < numOfScenarios; i++)
{
StochasticAssetPrice S1 = new StochasticAssetPrice(S);
double[][] PricePath;
PricePath = D.DipathByAntitheticMethod(S1, nrand, T, timeSteps);
Sample[i] = (ValueAtMaturity(PricePath[0][timeSteps])
+ ValueAtMaturity(PricePath[1][timeSteps])) / 2.0;
sumValue += Sample[i];
}
}
else
{
//when antithetic variance reduction technique is not used
for (int i = 0; i < numOfScenarios; i++)
{
StochasticAssetPrice S1 = new StochasticAssetPrice(S);
double[] PricePath;
PricePath = D.GeneratingRandomPricePath(S1, nrand, T, timeSteps);
Sample[i] = ValueAtMaturity(PricePath[timeSteps]);
sumValue += Sample[i];
}
}
double disFactor = Math.Exp(-S.Mu * T); //discount factor to convert value at maturity to current
Result[0] = sumValue / (double)numOfScenarios * disFactor;
double totalVariance = 0.0;
for (int i = 0; i < numOfScenarios; i++)
{
totalVariance += Math.Pow(Sample[i] - Result[0], 2.0);
}
if (numOfScenarios > 1)
{
double std = Math.Sqrt(totalVariance / (numOfScenarios - 1));
Result[1] = std / Math.Sqrt(numOfScenarios) * disFactor;
}
return(Result);
}
/// <summary>
/// override the <method>DipathByAntitheticMethod</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point
/// </summary>
public double[][] DipathByAntitheticMethod(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps)
{
double[][] pricePath = new double[2][];
pricePath[0] = new double[timeSteps + 1];
pricePath[1] = new double[timeSteps + 1];
StochasticAssetPrice S2 = new StochasticAssetPrice(S);
double dt = totalTime / (double)timeSteps;
pricePath[0][0] = S.CurrentPrice;
pricePath[1][0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
double z2 = -z;
pricePath[0][i] = GetNextPrice(S, dt, z);
pricePath[1][i] = GetNextPrice(S2, dt, z2);
}
return pricePath;
}
/// <summary>
/// override the <method>DipathByAntitheticMethod</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point
/// </summary>
public double[][] DipathByAntitheticMethod(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps)
{
double[][] pricePath = new double[2][];
pricePath[0] = new double[timeSteps + 1];
pricePath[1] = new double[timeSteps + 1];
StochasticAssetPrice S2 = new StochasticAssetPrice(S);
double dt = totalTime / (double)timeSteps;
pricePath[0][0] = S.CurrentPrice;
pricePath[1][0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
double z2 = -z;
pricePath[0][i] = GetNextPrice(S, dt, z);
pricePath[1][i] = GetNextPrice(S2, dt, z2);
}
return(pricePath);
}
/// <summary>
/// override the <method>GeneratingRandomPricePath</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point.
/// </summary>
public double[] GeneratingRandomPricePath(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps, bool visualizationFlag = false, Form1 form = null)
{
double[] pricePath = new double[timeSteps + 1];
double dt = totalTime / (double)timeSteps;
pricePath[0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
pricePath[i] = GetNextPrice(S, dt, z);
}
if (visualizationFlag & form != null)
{
double[] X = new double[timeSteps + 1];
for (int i = 0; i <= timeSteps; i++)
{
X[i] = i;
}
form.add(X, pricePath, "");
}
return(pricePath);
}
/// <summary>
/// override the <method>DipathByAntitheticMethod</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point
/// </summary>
public double[][] DipathByAntitheticMethod(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps, bool visualizationFlag = false, Form1 form = null)
{
double[][] pricePath = new double[2][];
pricePath[0] = new double[timeSteps + 1];
pricePath[1] = new double[timeSteps + 1];
StochasticAssetPrice S2 = new StochasticAssetPrice(S);
double dt = totalTime / (double)timeSteps;
pricePath[0][0] = S.CurrentPrice;
pricePath[1][0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
double z2 = -z;
pricePath[0][i] = GetNextPrice(S, dt, z);
pricePath[1][i] = GetNextPrice(S2, dt, z2);
}
if (visualizationFlag & form != null)
{
double[] X = new double[timeSteps + 1];
for (int i = 0; i <= timeSteps; i++)
{
X[i] = i;
}
form.add(X, pricePath[0], "");
form.add(X, pricePath[1], "");
}
return pricePath;
}
/// <summary>
/// override the <method>PricingByMCSim</method>
/// In each scenario, a price path is generated and the option value under
/// this scenario is only decided by the final price. So, we take the average
/// for the 'value at maturity' of all the simulated scenarios and
/// discounted as the approximation for the option value.
/// This method also outputs the standard error for the approximation.
/// </summary>
public override double[] PricingByMCSim(StochasticAssetPrice S, IDiscretizationScheme D, int numOfScenarios,
int timeSteps, bool antitheticFlag, bool visualizationFlag = false, Form1 form = null)
{
double[] Result = new double[2]; //record the approximated price and standard error
double[] Sample = new double[numOfScenarios]; //record value at maturity for each scenario
double sumValue = 0.0; //record cumulative sum of Sample array
GaussianGenerator nrand = new GaussianGenerator();
if (antitheticFlag)
{
//when antithetic variance reduction technique is used
for (int i = 0; i < numOfScenarios; i++)
{
StochasticAssetPrice S1 = new StochasticAssetPrice(S);
double[][] PricePath;
PricePath = D.DipathByAntitheticMethod(S1, nrand, T, timeSteps, visualizationFlag, form);
Sample[i] = (ValueAtMaturity(PricePath[0][timeSteps])
+ ValueAtMaturity(PricePath[1][timeSteps])) / 2.0;
sumValue += Sample[i];
}
}
else
{
//when antithetic variance reduction technique is not used
for (int i = 0; i < numOfScenarios; i++)
{
StochasticAssetPrice S1 = new StochasticAssetPrice(S);
double[] PricePath;
PricePath = D.GeneratingRandomPricePath(S1, nrand, T, timeSteps, visualizationFlag, form);
Sample[i] = ValueAtMaturity(PricePath[timeSteps]);
sumValue += Sample[i];
}
}
double disFactor = Math.Exp(-S.Mu * T); //discount factor to convert value at maturity to current
Result[0] = sumValue / (double)numOfScenarios * disFactor;
double totalVariance = 0.0;
for (int i = 0; i < numOfScenarios; i++)
{
totalVariance += Math.Pow(Sample[i] - Result[0], 2.0);
}
if (numOfScenarios > 1)
{
double std = Math.Sqrt(totalVariance / (numOfScenarios - 1));
Result[1] = std / Math.Sqrt(numOfScenarios) * disFactor;
}
return Result;
}
/// <summary>
/// override the <method>GeneratingRandomPricePath</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point.
/// </summary>
public double[] GeneratingRandomPricePath(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps, bool visualizationFlag = false, Form1 form = null)
{
double[] pricePath = new double[timeSteps + 1];
double dt = totalTime / (double)timeSteps;
pricePath[0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
pricePath[i] = GetNextPrice(S, dt, z);
}
if (visualizationFlag & form != null)
{
double[] X = new double[timeSteps + 1];
for (int i = 0; i <= timeSteps; i++)
{
X[i] = i;
}
form.add(X, pricePath, "");
}
return pricePath;
}
/// <summary>
/// override the <method>GeneratingRandomPricePath</method>.
/// For Black Scholes model, mu and sigma is constant, and only one random
/// variate is needed to generate the state for next point.
/// </summary>
public double[] GeneratingRandomPricePath(StochasticAssetPrice S, GaussianGenerator nrandom,
double totalTime, int timeSteps)
{
double[] pricePath = new double[timeSteps + 1];
double dt = totalTime / (double)timeSteps;
pricePath[0] = S.CurrentPrice;
for (int i = 1; i <= timeSteps; i++)
{
double z = nrandom.NextGaussian();
pricePath[i] = GetNextPrice(S, dt, z);
}
return pricePath;
}
