protected override void generateArguments()
{
double rho = arguments_[0].value(0.0);
for (int i = 0; i < size_; ++i)
{
for (int j = i; j < size_; ++j)
{
corrMatrix_[i, j] = corrMatrix_[j, i] = Math.Exp(-rho * Math.Abs((double)i - (double)j));
}
}
pseudoSqrt_ = MatrixUtilitites.pseudoSqrt(corrMatrix_, MatrixUtilitites.SalvagingAlgorithm.Spectral);
}
public StochasticProcessArray(List <StochasticProcess1D> processes, Matrix correlation)
{
processes_ = processes;
sqrtCorrelation_ = MatrixUtilitites.pseudoSqrt(correlation, MatrixUtilitites.SalvagingAlgorithm.Spectral);
Utils.QL_REQUIRE(processes.Count != 0, () => "no processes given");
Utils.QL_REQUIRE(correlation.rows() == processes.Count, () =>
"mismatch between number of processes and size of correlation matrix");
for (int i = 0; i < processes_.Count; i++)
{
processes_[i].registerWith(update);
}
}
protected override void generateArguments()
{
double rho = arguments_[0].value(0.0);
double beta = arguments_[1].value(0.0);
for (int i = 0; i < size_; ++i)
{
for (int j = i; j < size_; ++j)
{
corrMatrix_[i, j] = corrMatrix_[j, i]
= rho + (1 - rho) * Math.Exp(-beta * Math.Abs((double)i - (double)j));
}
}
pseudoSqrt_ = MatrixUtilitites.rankReducedSqrt(corrMatrix_, factors_, 1.0, MatrixUtilitites.SalvagingAlgorithm.None);
corrMatrix_ = pseudoSqrt_ * Matrix.transpose(pseudoSqrt_);
}
public StochasticProcessArray(List <StochasticProcess1D> processes, Matrix correlation)
{
processes_ = processes;
sqrtCorrelation_ = MatrixUtilitites.pseudoSqrt(correlation, MatrixUtilitites.SalvagingAlgorithm.Spectral);
if (processes.Count == 0)
{
throw new ApplicationException("no processes given");
}
if (correlation.rows() != processes.Count)
{
throw new ApplicationException("mismatch between number of processes and size of correlation matrix");
}
for (int i = 0; i < processes_.Count; i++)
{
processes_[i].registerWith(update);
}
}
public LfmHullWhiteParameterization(
LiborForwardModelProcess process,
OptionletVolatilityStructure capletVol,
Matrix correlation, int factors)
: base(process.size(), factors)
{
diffusion_ = new Matrix(size_ - 1, factors_);
fixingTimes_ = process.fixingTimes();
Matrix sqrtCorr = new Matrix(size_ - 1, factors_, 1.0);
if (correlation.empty())
{
if (!(factors_ == 1))
{
throw new ApplicationException("correlation matrix must be given for " +
"multi factor models");
}
}
else
{
if (!(correlation.rows() == size_ - 1 &&
correlation.rows() == correlation.columns()))
{
throw new ApplicationException("wrong dimesion of the correlation matrix");
}
if (!(factors_ <= size_ - 1))
{
throw new ApplicationException("too many factors for given LFM process");
}
Matrix tmpSqrtCorr = MatrixUtilitites.pseudoSqrt(correlation,
MatrixUtilitites.SalvagingAlgorithm.Spectral);
// reduce to n factor model
// "Reconstructing a valid correlation matrix from invalid data"
// (<http://www.quarchome.org/correlationmatrix.pdf>)
for (int i = 0; i < size_ - 1; ++i)
{
double d = 0;
tmpSqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => d += vv * tmpSqrtCorr.row(i)[ii]);
//sqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => sqrtCorr.row(i)[ii] = tmpSqrtCorr.row(i).GetRange(0, factors_)[ii] / Math.Sqrt(d));
for (int k = 0; k < factors_; ++k)
{
sqrtCorr[i, k] = tmpSqrtCorr.row(i).GetRange(0, factors_)[k] / Math.Sqrt(d);
}
}
}
List <double> lambda = new List <double>();
DayCounter dayCounter = process.index().dayCounter();
List <double> fixingTimes = process.fixingTimes();
List <Date> fixingDates = process.fixingDates();
for (int i = 1; i < size_; ++i)
{
double cumVar = 0.0;
for (int j = 1; j < i; ++j)
{
cumVar += lambda[i - j - 1] * lambda[i - j - 1]
* (fixingTimes[j + 1] - fixingTimes[j]);
}
double vol = capletVol.volatility(fixingDates[i], 0.0, false);
double var = vol * vol
* capletVol.dayCounter().yearFraction(fixingDates[0],
fixingDates[i]);
lambda.Add(Math.Sqrt((var - cumVar)
/ (fixingTimes[1] - fixingTimes[0])));
for (int q = 0; q < factors_; ++q)
{
diffusion_[i - 1, q] = sqrtCorr[i - 1, q] * lambda.Last();
}
}
covariance_ = diffusion_ * Matrix.transpose(diffusion_);
}
public virtual Matrix pseudoSqrt(double t, Vector x = null)
{
return(MatrixUtilitites.pseudoSqrt(this.correlation(t, x),
MatrixUtilitites.SalvagingAlgorithm.Spectral));
}
