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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/legacy/libormarketmodels/lfmcovarproxy.hpp>
#include <ql/math/integrals/kronrodintegral.hpp>
namespace QuantLib {
LfmCovarianceProxy::LfmCovarianceProxy(
const boost::shared_ptr<LmVolatilityModel>& volaModel,
const boost::shared_ptr<LmCorrelationModel>& corrModel)
: LfmCovarianceParameterization(corrModel->size(), corrModel->factors()),
volaModel_(volaModel),
corrModel_(corrModel) {
QL_REQUIRE(volaModel_->size() == corrModel_->size(),
"different size for the volatility (" << volaModel_->size() <<
") and correlation (" << corrModel_->size() <<
") models");
}
boost::shared_ptr<LmVolatilityModel>
LfmCovarianceProxy::volatilityModel() const {
return volaModel_;
}
boost::shared_ptr<LmCorrelationModel>
LfmCovarianceProxy::correlationModel() const {
return corrModel_;
}
Disposable<Matrix> LfmCovarianceProxy::diffusion(Time t,
const Array& x) const {
Matrix pca = corrModel_->pseudoSqrt(t, x);
Array vol = volaModel_->volatility(t, x);
for (Size i=0; i<size_; ++i) {
std::transform(pca.row_begin(i), pca.row_end(i),
pca.row_begin(i),
std::bind2nd(std::multiplies<Real>(), vol[i]));
}
return pca;
}
Disposable<Matrix> LfmCovarianceProxy::covariance(Time t,
const Array& x) const {
Array volatility = volaModel_->volatility(t, x);
Matrix correlation = corrModel_->correlation(t, x);
Matrix tmp(size_, size_);
for (Size i=0; i<size_; ++i) {
for (Size j=0; j<size_; ++j) {
tmp[i][j] = volatility[i]*correlation[i][j]*volatility[j];
}
}
return tmp;
}
class LfmCovarianceProxy::Var_Helper {
public:
Var_Helper(const LfmCovarianceProxy* proxy, Size i, Size j);
Real operator()(Real t) const;
private:
const Size i_, j_;
const LmVolatilityModel* const volaModel_;
const LmCorrelationModel* const corrModel_;
};
LfmCovarianceProxy::Var_Helper::Var_Helper(const LfmCovarianceProxy* proxy,
Size i, Size j)
: i_(i),
j_(j),
volaModel_(proxy->volaModel_.get()),
corrModel_(proxy->corrModel_.get()) {
}
Real LfmCovarianceProxy::Var_Helper::operator()(Real t) const {
Volatility v1, v2;
if (i_ == j_) {
v1 = v2 = volaModel_->volatility(i_, t);
} else {
v1 = volaModel_->volatility(i_, t);
v2 = volaModel_->volatility(j_, t);
}
return v1 * corrModel_->correlation(i_, j_, t) * v2;
}
Real LfmCovarianceProxy::integratedCovariance(
Size i, Size j, Time t, const Array& x) const {
if (corrModel_->isTimeIndependent()) {
try {
// if all objects support these methods
// thats by far the fastest way to get the
// integrated covariance
return corrModel_->correlation(i, j, 0.0, x)
* volaModel_->integratedVariance(j, i, t, x);
}
catch (Error&) {
// okay proceed with the
// slow numerical integration routine
}
}
QL_REQUIRE(x.empty(), "can not handle given x here");
Real tmp=0.0;
Var_Helper helper(this, i, j);
GaussKronrodAdaptive integrator(1e-10, 10000);
for (Size k=0; k<64; ++k) {
tmp+=integrator(helper, k*t/64., (k+1)*t/64.);
}
return tmp;
}
}
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