public LfmHullWhiteParameterization(
LiborForwardModelProcess process,
OptionletVolatilityStructure capletVol)
: this(process, capletVol, new Matrix(), 1)
{
}
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())
{
Utils.QL_REQUIRE(factors_ == 1, () => "correlation matrix must be given for multi factor models");
}
else
{
Utils.QL_REQUIRE(correlation.rows() == size_ - 1 &&
correlation.rows() == correlation.columns(), () => "wrong dimesion of the correlation matrix");
Utils.QL_REQUIRE(factors_ <= size_ - 1, () => "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]);
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_);
}