public void ProbaMeasure(double lambda, RrFunction sigma, Duration probaMaturity, Duration simulationMaturity,
int quadratureNbPoints, double precision)
{
var refDate = DateTime.Parse("07/06/2009");
var hw1 = new Hw1Model(TimeMeasure.Act365(refDate), Currency.Eur, lambda, sigma);
var probaMeasure = new PaymentInfo(hw1.Currency, refDate + probaMaturity);
var t = refDate + simulationMaturity;
var hw1PathGen = new Hw1ModelPathGeneratorFactory().Build(hw1, null, probaMeasure, new[] { t });
var brownianBridge = BrownianBridge.Create(hw1PathGen.AllSimulatedDates);
var hw1Zc = new Hw1ModelZcRepresentation(hw1);
var numeraireZc = hw1Zc.Zc(t, probaMeasure.Date, 1.0);
Assert.AreEqual(hw1PathGen.AllSimulatedDates.Length, 1);
double[] x, w;
GaussHermite.GetQuadrature(quadratureNbPoints, out x, out w);
double flow = 0.0;
for (int i = 0; i < x.Length; i++)
{
var dw = brownianBridge.PathIncrements(new[] { x[i] }, 1);
var ornstein = hw1PathGen.Path(dw).GetProcessValue(0);
flow += w[i] * 1.0 / numeraireZc.Eval(ornstein);
}
var error = Math.Abs(flow - 1.0);
Assert.LessOrEqual(error, precision);
}
public void SinglePathCovariance(double[] dates, double epsilon, double precision)
{
var brownian = BrownianBridge.Create(dates);
var dim = brownian.GaussianSize(1);
var jacobian = FiniteDifferenceUtils.CenteredJacobian(x => BrownianPath1d(brownian, x), dim, new double[dim], epsilon);
var covariance = jacobian.Prod(jacobian.Tranpose());
for (int i = 0; i < dates.Length; i++)
{
for (int j = 0; j < dates.Length; j++)
{
var cov_ij = Math.Min(dates[i], dates[j]);
var error = Math.Abs(cov_ij - covariance[i, j]);
Assert.LessOrEqual(error, precision);
}
}
}
public McModel Build(IModel model, Market market, DateTime[] simulatedDates)
{
PaymentInfo probaMeasure = ProbaMeasure(simulatedDates, model);
var factorRepresentationFactory = FactorRepresentationFactories.For(model);
IFactorModelRepresentation factorRepresentation = factorRepresentationFactory.Build(model, market, probaMeasure);
var modelPathGenFactory = ModelPathGeneratorFactories.For(model, mcConfig);
IProcessPathGenerator processPathGenerator = modelPathGenFactory.Build(model, market, probaMeasure, simulatedDates);
BrownianBridge brownianBridge = BrownianBridge.Create(processPathGenerator.AllSimulatedDates);
int randomDim = brownianBridge.GaussianSize(processPathGenerator.ProcessDim);
IRandomGenerator randomGenerator = mcConfig.RandomGenerator.Build(randomDim);
double numeraire0 = market.DiscountCurve(probaMeasure.Financing).Zc(probaMeasure.Date);
return(new McModel(factorRepresentation, simulatedDates,
randomGenerator, brownianBridge, processPathGenerator,
probaMeasure, numeraire0));
}
public void SinglePathIncrementCovariance(double[] dates, double epsilon, double precision)
{
var brownian = BrownianBridge.Create(dates);
var dim = brownian.GaussianSize(1);
var jacobian = FiniteDifferenceUtils.CenteredJacobian(x => PathInc1D(brownian, x), dim, new double[dim], epsilon);
var covariance = jacobian.Prod(jacobian.Tranpose());
for (int i = 0; i < dates.Length; i++)
{
var error = Math.Abs(covariance[i, i] - (i == 0 ? dates[0] : dates[i] - dates[i - 1]));
Assert.LessOrEqual(error, precision);
for (int j = 0; j < i; j++)
{
var errorij = Math.Abs(covariance[i, j]);
Assert.LessOrEqual(errorij, precision);
Assert.IsTrue(DoubleUtils.MachineEquality(covariance[i, j], covariance[j, i]));
}
}
}