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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Ferdinando Ametrano
Copyright (C) 2007 Marco Bianchetti
Copyright (C) 2007 Giorgio Facchinetti
Copyright (C) 2007 Franois du Vignaud
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/models/marketmodels/correlations/expcorrelations.hpp>
#include <ql/models/marketmodels/correlations/timehomogeneousforwardcorrelation.hpp>
#include <ql/models/marketmodels/utilities.hpp>
#include <ql/math/comparison.hpp>
#include <ql/utilities/dataformatters.hpp>
namespace QuantLib {
Disposable<Matrix> exponentialCorrelations(
const std::vector<Time>& rateTimes,
Real longTermCorr,
Real beta,
Real gamma,
Time time) {
// preliminary checks
checkIncreasingTimes(rateTimes);
QL_REQUIRE(longTermCorr<=1.0 && longTermCorr>=0.0,
"Long term correlation (" << longTermCorr <<
") outside [0;1] interval");
QL_REQUIRE(beta>=0.0,
"beta (" << beta <<
") must be greater than zero");
QL_REQUIRE(gamma<=1.0 && gamma>=0.0,
"gamma (" << gamma <<
") outside [0;1] interval");
// Calculate correlation matrix
Size nbRows = rateTimes.size()-1;
Matrix correlations(nbRows, nbRows, 0.0);
for (Size i=0; i<nbRows; ++i) {
// correlation is defined only between
// (alive) stochastic rates...
if (time<=rateTimes[i]) {
correlations[i][i] = 1.0;
for (Size j=0; j<i; ++j) {
if (time<=rateTimes[j]) {
correlations[i][j] = correlations[j][i] =
longTermCorr + (1.0-longTermCorr) *
std::exp(-beta*std::fabs(
std::pow(rateTimes[i]-time, gamma) -
std::pow(rateTimes[j]-time, gamma)
)
);
}
}
}
}
return correlations;
}
ExponentialForwardCorrelation::ExponentialForwardCorrelation(
const std::vector<Time>& rateTimes,
Real longTermCorr,
Real beta,
Real gamma,
const std::vector<Time>& times)
: numberOfRates_(rateTimes.empty() ? 0 : rateTimes.size()-1),
longTermCorr_(longTermCorr), beta_(beta), gamma_(gamma),
rateTimes_(rateTimes),
times_(times) {
QL_REQUIRE(numberOfRates_>1,
"Rate times must contain at least two values");
checkIncreasingTimes(rateTimes_);
// corrTimes must include all rateTimes but the last
if (times_ == std::vector<Time>())
times_ = std::vector<Time>(rateTimes_.begin(),
rateTimes_.end()-1);
else
checkIncreasingTimes(times_);
if (close(gamma,1.0)) {
std::vector<Time> temp(rateTimes_.begin(), rateTimes_.end()-1);
QL_REQUIRE(times_==temp,
"corr times " << io::sequence(times_)
<< " must be equal to (all) rate times (but the last) "
<< io::sequence(temp));
Matrix c = exponentialCorrelations(
rateTimes_, longTermCorr_, beta_, 1.0, 0.0);
correlations_ =
TimeHomogeneousForwardCorrelation::evolvedMatrices(c);
} else {
// FIXME should check here that all rateTimes but the last
// are included in rateTimes
QL_REQUIRE(times_.back()<=rateTimes_[numberOfRates_],
"last corr time " << times_.back() <<
"is after next-to-last rate time " <<
rateTimes_[numberOfRates_]);
correlations_.resize(times_.size());
Time time = times_[0]/2.0;
correlations_[0] = exponentialCorrelations(
rateTimes_, longTermCorr_, beta_, gamma_, time);
for (Size k=1; k<times_.size(); ++k) {
time = (times_[k]+times_[k-1])/2.0;
correlations_[k] = exponentialCorrelations(
rateTimes_, longTermCorr_, beta_, gamma_, time);
}
}
}
const std::vector<Time>&
ExponentialForwardCorrelation::times() const {
return times_;
}
const std::vector<Time>&
ExponentialForwardCorrelation::rateTimes() const {
return rateTimes_;
}
const std::vector<Matrix>&
ExponentialForwardCorrelation::correlations() const {
return correlations_;
}
Size ExponentialForwardCorrelation::numberOfRates() const {
return numberOfRates_;
}
}
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