public Matrix(Matrix from)
{
data_ = !from.empty() ? (double[])from.data_.Clone() : null;
rows_ = from.rows_;
columns_ = from.columns_;
}
LiborForwardModelProcess makeProcess(Matrix volaComp)
{
int factors = (volaComp.empty() ? 1 : volaComp.columns());
IborIndex index = makeIndex();
LiborForwardModelProcess process= new LiborForwardModelProcess(len, index,null);
LfmCovarianceParameterization fct=new LfmHullWhiteParameterization(
process,
makeCapVolCurve(Settings.evaluationDate()),
volaComp * Matrix.transpose(volaComp), factors);
process.setCovarParam(fct);
return process;
}
public Matrix(Matrix from) {
data_ = !from.empty() ? (double[])from.data_.Clone() : null;
rows_ = from.rows_;
columns_ = from.columns_;
}
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 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_);
}
