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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2005, 2006 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/math/matrixutilities/pseudosqrt.hpp>
#include <ql/legacy/libormarketmodels/lfmhullwhiteparam.hpp>
namespace QuantLib {
LfmHullWhiteParameterization::LfmHullWhiteParameterization(
const boost::shared_ptr<LiborForwardModelProcess> & process,
const boost::shared_ptr<OptionletVolatilityStructure> & capletVol,
const Matrix& correlation, Size factors)
: LfmCovarianceParameterization(process->size(), factors),
diffusion_ (size_-1, factors_),
fixingTimes_(process->fixingTimes()) {
Matrix sqrtCorr(size_-1, factors_, 1.0);
if (correlation.empty()) {
QL_REQUIRE(factors_ == 1,
"correlation matrix must be given for "
"multi factor models");
} else {
QL_REQUIRE( correlation.rows() == size_-1
&& correlation.rows() == correlation.columns(),
"wrong dimesion of the correlation matrix");
QL_REQUIRE(factors_ <= size_-1,
"too many factors for given LFM process");
Matrix tmpSqrtCorr = pseudoSqrt(correlation,
SalvagingAlgorithm::Spectral);
// reduce to n factor model
// "Reconstructing a valid correlation matrix from invalid data"
// (<http://www.quarchome.org/correlationmatrix.pdf>)
for (Size i=0; i < size_-1; ++i) {
std::transform(
tmpSqrtCorr[i], tmpSqrtCorr[i]+factors_, sqrtCorr[i],
std::bind2nd(std::divides<Real>(),
std::sqrt(std::inner_product(
tmpSqrtCorr[i],tmpSqrtCorr[i]+factors_,
tmpSqrtCorr[i], 0.0))));
}
}
std::vector<Volatility> lambda;
const DayCounter dayCounter = process->index()->dayCounter();
const std::vector<Time> fixingTimes = process->fixingTimes();
const std::vector<Date> fixingDates = process->fixingDates();
for (Size i = 1; i < size_; ++i) {
double cumVar = 0.0;
for (Size j = 1; j < i; ++j) {
cumVar += lambda[i-j-1] * lambda[i-j-1]
* (fixingTimes[j+1] - fixingTimes[j]);
}
const Volatility vol = capletVol->volatility(fixingDates[i], 0.0);
const Volatility var = vol * vol
* capletVol->dayCounter().yearFraction(fixingDates[0],
fixingDates[i]);
lambda.push_back(std::sqrt( (var - cumVar)
/ (fixingTimes[1] - fixingTimes[0])) );
for (Size q=0; q<factors_; ++q) {
diffusion_[i-1][q] = sqrtCorr[i-1][q] * lambda.back();
}
}
covariance_ = diffusion_ * transpose(diffusion_);
}
Size LfmHullWhiteParameterization::nextIndexReset(Time t) const {
return std::upper_bound(fixingTimes_.begin(), fixingTimes_.end(), t)
- fixingTimes_.begin();
}
Disposable<Matrix> LfmHullWhiteParameterization::diffusion(
Time t, const Array&) const {
Matrix tmp(size_, factors_, 0.0);
const Size m = nextIndexReset(t);
for (Size k=m; k<size_; ++k) {
for (Size q=0; q<factors_; ++q) {
tmp[k][q] = diffusion_[k-m][q];
}
}
return tmp;
}
Disposable<Matrix> LfmHullWhiteParameterization::covariance(
Time t, const Array&) const {
Matrix tmp(size_, size_, 0.0);
const Size m = nextIndexReset(t);
for (Size k=m; k<size_; ++k) {
for (Size i=m; i<size_; ++i) {
tmp[k][i] = covariance_[k-m][i-m];
}
}
return tmp;
}
Disposable<Matrix> LfmHullWhiteParameterization::integratedCovariance(
Time t, const Array&) const {
Matrix tmp(size_, size_, 0.0);
Size last = std::lower_bound(fixingTimes_.begin(),
fixingTimes_.end(), t)
- fixingTimes_.begin();
for (Size i=0; i<last; ++i) {
const Time dt = ((i+1<last)? fixingTimes_[i+1] : t )
- fixingTimes_[i];
for (Size k=i; k<size_-1; ++k) {
for (Size l=i; l<size_-1; ++l) {
tmp[k+1][l+1]+= covariance_[k-i][l-i]*dt;
}
}
}
return tmp;
}
}
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