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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Giorgio Facchinetti
Copyright (C) 2007 Chiara Fornarola
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/driftcomputation/lmmnormaldriftcalculator.hpp>
namespace QuantLib {
LMMNormalDriftCalculator::LMMNormalDriftCalculator(const Matrix& pseudo,
const std::vector<Time>& taus,
Size numeraire,
Size alive)
: numberOfRates_(taus.size()), numberOfFactors_(pseudo.columns()),
isFullFactor_(numberOfFactors_ == numberOfRates_), numeraire_(numeraire), alive_(alive),
oneOverTaus_(taus.size()), pseudo_(pseudo), tmp_(taus.size(), 0.0),
e_(pseudo_.columns(), pseudo_.rows(), 0.0), downs_(taus.size()), ups_(taus.size()) {
// Check requirements
QL_REQUIRE(numberOfRates_>0, "Dim out of range");
QL_REQUIRE(pseudo.rows()==numberOfRates_,
"pseudo.rows() not consistent with dim");
QL_REQUIRE(pseudo.columns()>0 && pseudo.columns()<=numberOfRates_,
"pseudo.rows() not consistent with pseudo.columns()");
QL_REQUIRE(alive<numberOfRates_, "Alive out of bounds");
QL_REQUIRE(numeraire_<=numberOfRates_, "Numeraire larger than dim");
QL_REQUIRE(numeraire_>=alive, "Numeraire smaller than alive");
// Precompute 1/taus
for (Size i=0; i<taus.size(); ++i)
oneOverTaus_[i] = 1.0/taus[i];
// Compute covariance matrix from pseudoroot
Matrix pT = transpose(pseudo_);
C_ = pseudo_*pT;
// Compute lower and upper extrema for (non reduced) drift calculation
for (Size i=alive_; i<numberOfRates_; ++i) {
downs_[i] = std::min(i+1, numeraire_);
ups_[i] = std::max(i+1, numeraire_);
}
}
void LMMNormalDriftCalculator::compute(const LMMCurveState& cs,
std::vector<Real>& drifts) const {
compute(cs.forwardRates(), drifts);
}
void LMMNormalDriftCalculator::compute(const std::vector<Rate>& fwds,
std::vector<Real>& drifts) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(fwds.size()==numberOfRates_, "numberOfRates <> dim");
QL_REQUIRE(drifts.size()==numberOfRates_, "drifts.size() <> dim");
#endif
if (isFullFactor_)
computePlain(fwds, drifts);
else
computeReduced(fwds, drifts);
}
void LMMNormalDriftCalculator::computePlain(const LMMCurveState& cs,
std::vector<Real>& drifts) const {
computePlain(cs.forwardRates(), drifts);
}
void LMMNormalDriftCalculator::computePlain(const std::vector<Rate>& forwards,
std::vector<Real>& drifts) const {
// Compute drifts without factor reduction,
// using directly the covariance matrix.
// Precompute forwards factor
Size i;
for(i=alive_; i<numberOfRates_; ++i)
tmp_[i] = 1.0/(oneOverTaus_[i]+forwards[i]);
// Compute drifts
for (i=alive_; i<numberOfRates_; ++i) {
drifts[i] = std::inner_product(tmp_.begin()+downs_[i],
tmp_.begin()+ups_[i],
C_.row_begin(i)+downs_[i], Real(0.0));
if (numeraire_>i+1)
drifts[i] = -drifts[i];
}
}
void LMMNormalDriftCalculator::computeReduced(const LMMCurveState& cs,
std::vector<Real>& drifts) const {
computeReduced(cs.forwardRates(), drifts);
}
void LMMNormalDriftCalculator::computeReduced(const std::vector<Rate>& forwards,
std::vector<Real>& drifts) const {
// Compute drifts with factor reduction,
// using the pseudo square root of the covariance matrix.
// Precompute forwards factor
for (Size i=alive_; i<numberOfRates_; ++i)
tmp_[i] = 1.0/(oneOverTaus_[i]+forwards[i]);
// Enforce initialization
for (Size r=0; r<numberOfFactors_; ++r)
e_[r][std::max(0,static_cast<Integer>(numeraire_)-1)] = 0.0;
// Now compute drifts: take the numeraire P_N (numeraire_=N)
// as the reference point, divide the summation into 3 steps,
// et impera:
// 1st step: the drift corresponding to the numeraire P_N is zero.
// (if N=0 no drift is null, if N=numberOfRates_ the last drift is null).
if (numeraire_>0) drifts[numeraire_-1] = 0.0;
// 2nd step: then, move backward from N-2 (included) back to
// alive (included) (if N=0 jumps to 3rd step, if N=numberOfRates_ the
// e_[r][N-1] are correctly initialized):
for (Integer i=static_cast<Integer>(numeraire_)-2;
i>=static_cast<Integer>(alive_); --i) {
drifts[i] = 0.0;
for (Size r=0; r<numberOfFactors_; ++r) {
e_[r][i] = e_[r][i+1] + tmp_[i+1] * pseudo_[i+1][r];
drifts[i] -= e_[r][i]*pseudo_[i][r];
}
}
// 3rd step: now, move forward from N (included) up to n (excluded)
// (if N=0 this is the only relevant computation):
for (Size i=numeraire_; i<numberOfRates_; ++i) {
drifts[i] = 0.0;
for (Size r=0; r<numberOfFactors_; ++r) {
if (i==0)
e_[r][i] = tmp_[i] * pseudo_[i][r];
else
e_[r][i] = e_[r][i-1] + tmp_[i] * pseudo_[i][r];
drifts[i] += e_[r][i]*pseudo_[i][r];
}
}
}
}
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