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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Mark Joshi
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
<https://www.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/pathwisegreeks/ratepseudorootjacobian.hpp>
#include <utility>
namespace QuantLib
{
RatePseudoRootJacobianNumerical::RatePseudoRootJacobianNumerical(const Matrix& pseudoRoot,
Size aliveIndex,
Size numeraire,
const std::vector<Time>& taus,
const std::vector<Matrix>& pseudoBumps,
const std::vector<Spread>& displacements)
:
pseudoRoot_(pseudoRoot),
aliveIndex_(aliveIndex),
taus_(taus),
displacements_(displacements),
numberBumps_(pseudoBumps.size()),
factors_(pseudoRoot.columns()),
drifts_(taus.size()),
bumpedRates_(taus.size())
{
Size numberRates= taus.size();
QL_REQUIRE(pseudoRoot_.rows()==numberRates,
"pseudoRoot_.rows()<> taus.size()");
QL_REQUIRE(displacements_.size()==numberRates,
"displacements_.size()<> taus.size()");
QL_REQUIRE(drifts_.size()==numberRates,
"drifts_.size()<> taus.size()");
for (Size i=0; i < pseudoBumps.size(); ++i)
{
QL_REQUIRE(pseudoBumps[i].rows()==numberRates,
"pseudoBumps[i].rows()<> taus.size() with i =" << i);
QL_REQUIRE(pseudoBumps[i].columns()==factors_,
"pseudoBumps[i].columns()<> factors with i = " << i);
Matrix pseudo(pseudoRoot_);
pseudo += pseudoBumps[i];
pseudoBumped_.push_back(pseudo);
driftsComputers_.emplace_back(pseudo, displacements, taus, numeraire, aliveIndex);
}
}
void RatePseudoRootJacobianNumerical::getBumps(const std::vector<Rate>& oldRates,
const std::vector<Real>& , // not used in the numerical implementation
const std::vector<Rate>& newRates,
const std::vector<Real>& gaussians,
Matrix& B)
{
Size numberRates = taus_.size();
QL_REQUIRE(B.rows()==numberBumps_,
"B.rows()<> numberBumps_");
QL_REQUIRE(B.columns()==taus_.size(),
"B.columns()<> number of rates");
for (Size i =0; i < numberBumps_; ++i)
{
const Matrix& pseudo = pseudoBumped_[i];
driftsComputers_[i].compute(oldRates,
drifts_);
for (Size j =0; j < aliveIndex_; ++j)
B[i][j]=0.0;
for (Size j=aliveIndex_; j < numberRates; ++j)
{
bumpedRates_[j] = std::log(oldRates[j]+displacements_[j]);
for (Size k=0; k < factors_; ++k)
bumpedRates_[j] += -0.5*pseudo[j][k]*pseudo[j][k];
bumpedRates_[j] +=drifts_[j];
for (Size k=0; k < factors_; ++k)
bumpedRates_[j] += pseudo[j][k]*gaussians[k];
bumpedRates_[j] = std::exp(bumpedRates_[j]);
bumpedRates_[j] -= displacements_[j];
Real tmp = bumpedRates_[j] - newRates[j];
B[i][j] = tmp;
}
}
}
RatePseudoRootJacobian::RatePseudoRootJacobian(const Matrix& pseudoRoot,
Size aliveIndex,
Size numeraire,
const std::vector<Time>& taus,
const std::vector<Matrix>& pseudoBumps,
std::vector<Spread> displacements)
: pseudoRoot_(pseudoRoot), aliveIndex_(aliveIndex), taus_(taus), pseudoBumps_(pseudoBumps),
displacements_(std::move(displacements)), numberBumps_(pseudoBumps.size()),
factors_(pseudoRoot.columns()),
// bumpedRates_(taus.size()),
e_(pseudoRoot.rows(), pseudoRoot.columns()), ratios_(taus_.size()) {
Size numberRates= taus.size();
QL_REQUIRE(aliveIndex == numeraire,
"we can do only do discretely compounding MM acount so aliveIndex must equal numeraire");
QL_REQUIRE(pseudoRoot_.rows()==numberRates,
"pseudoRoot_.rows()<> taus.size()");
QL_REQUIRE(displacements_.size()==numberRates,
"displacements_.size()<> taus.size()");
for (Size i=0; i < pseudoBumps.size(); ++i)
{
QL_REQUIRE(pseudoBumps[i].rows()==numberRates,
"pseudoBumps[i].rows()<> taus.size() with i =" << i);
QL_REQUIRE(pseudoBumps[i].columns()==factors_,
"pseudoBumps[i].columns()<> factors with i = " << i);
}
for (Size i=0; i < numberRates; ++i)
{
allDerivatives_.emplace_back(numberRates, factors_);
}
}
void RatePseudoRootJacobian::getBumps(const std::vector<Rate>& oldRates,
const std::vector<Real>& discountRatios,
const std::vector<Rate>& newRates,
const std::vector<Real>& gaussians,
Matrix& B)
{
Size numberRates = taus_.size();
QL_REQUIRE(B.rows() == numberBumps_, "we need B.rows() which is " << B.rows() << " to equal numberBumps_ which is " << numberBumps_);
QL_REQUIRE(B.columns() == numberRates, "we need B.columns() which is " << B.columns() << " to equal numberRates which is " << numberRates);
for (Size j=aliveIndex_; j < numberRates; ++j)
ratios_[j] = (oldRates[j] + displacements_[j])*discountRatios[j+1];
for (Size f=0; f < factors_; ++f)
{
e_[aliveIndex_][f] = 0;
for (Size j= aliveIndex_+1; j < numberRates; ++j)
e_[j][f] = e_[j-1][f] + ratios_[j-1]*pseudoRoot_[j-1][f];
}
for (Size f=0; f < factors_; ++f)
for (Size j=aliveIndex_; j < numberRates; ++j)
{
for (Size k= aliveIndex_; k < j ; ++k)
allDerivatives_[j][k][f] = newRates[j]*ratios_[k]*taus_[k]*pseudoRoot_[j][f];
// GG don't seem to have the 2, this term is miniscule in any case
Real tmp = //2*
2*ratios_[j]*taus_[j]*pseudoRoot_[j][f];
tmp -= pseudoRoot_[j][f];
tmp += e_[j][f]*taus_[j];
tmp += gaussians[f];
tmp *= (newRates[j]+displacements_[j]);
allDerivatives_[j][j][f] =tmp;
for (Size k= j+1; k < numberRates ; ++k)
allDerivatives_[j][k][f]=0.0;
}
for (Size i =0; i < numberBumps_; ++i)
{
Size j=0;
for (; j < aliveIndex_; ++j)
{
B[i][j]=0.0;
}
for (; j < numberRates; ++j)
{
Real sum =0.0;
for (Size k=aliveIndex_; k < numberRates; ++k)
for (Size f=0; f < factors_; ++f)
sum += pseudoBumps_[i][k][f]*allDerivatives_[j][k][f];
B[i][j] =sum;
}
}
}
RatePseudoRootJacobianAllElements::RatePseudoRootJacobianAllElements(
const Matrix& pseudoRoot,
Size aliveIndex,
Size numeraire,
const std::vector<Time>& taus,
std::vector<Spread> displacements)
: pseudoRoot_(pseudoRoot), aliveIndex_(aliveIndex), taus_(taus),
displacements_(std::move(displacements)), factors_(pseudoRoot.columns()),
// bumpedRates_(taus.size()),
e_(pseudoRoot.rows(), pseudoRoot.columns()), ratios_(taus_.size()) {
Size numberRates= taus.size();
QL_REQUIRE(aliveIndex == numeraire,
"we can do only do discretely compounding MM acount so aliveIndex must equal numeraire");
QL_REQUIRE(pseudoRoot_.rows()==numberRates,
"pseudoRoot_.rows()<> taus.size()");
QL_REQUIRE(displacements_.size()==numberRates,
"displacements_.size()<> taus.size()");
}
void RatePseudoRootJacobianAllElements::getBumps(const std::vector<Rate>& oldRates,
const std::vector<Real>& discountRatios,
const std::vector<Rate>& newRates,
const std::vector<Real>& gaussians,
std::vector<Matrix>& B)
{
Size numberRates = taus_.size();
QL_REQUIRE(B.size() == numberRates, "we need B.size() which is " << B.size() << " to equal numberRates which is " << numberRates);
for (auto& j : B)
QL_REQUIRE(j.columns() == factors_ && j.rows() == numberRates,
"we need B[j].rows() which is "
<< j.rows() << " to equal numberRates which is " << numberRates
<< " and B[j].columns() which is " << j.columns()
<< " to be equal to factors which is " << factors_);
for (Size j = aliveIndex_; j < numberRates; ++j)
ratios_[j] = (oldRates[j] + displacements_[j]) * discountRatios[j + 1];
for (Size f = 0; f < factors_; ++f) {
e_[aliveIndex_][f] = 0;
for (Size j = aliveIndex_ + 1; j < numberRates; ++j)
e_[j][f] = e_[j - 1][f] + ratios_[j - 1] * pseudoRoot_[j - 1][f];
}
// nullify B for rates that have already reset
for (Size j=0; j < aliveIndex_; ++j)
for (Size k=0; k < numberRates; ++k)
for (Size f=0; f < factors_; ++f)
B[j][k][f] =0.0;
for (Size f=0; f < factors_; ++f)
for (Size j=aliveIndex_; j < numberRates; ++j)
{
for (Size k= aliveIndex_; k < j ; ++k)
B[j][k][f] = newRates[j]*ratios_[k]*taus_[k]*pseudoRoot_[j][f];
Real tmp = 2*ratios_[j]*taus_[j]*pseudoRoot_[j][f];
tmp -= pseudoRoot_[j][f];
tmp += e_[j][f]*taus_[j];
tmp += gaussians[f];
tmp *= (newRates[j]+displacements_[j]);
B[j][j][f] =tmp;
for (Size k= 0; k < aliveIndex_ ; ++k)
B[j][k][f]=0.0;
for (Size k= j+1; k < numberRates ; ++k)
B[j][k][f]=0.0;
}
}
}
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