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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 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/driftcomputation/smmdriftcalculator.hpp>
#include <ql/models/marketmodels/curvestates/coterminalswapcurvestate.hpp>
namespace QuantLib {
SMMDriftCalculator::SMMDriftCalculator(
const Matrix& pseudo,
const std::vector<Spread>& displacements,
const std::vector<Time>& taus,
Size numeraire,
Size alive)
: numberOfRates_(taus.size()), numberOfFactors_(pseudo.columns()),
numeraire_(numeraire), alive_(alive),
displacements_(displacements), oneOverTaus_(taus.size()),
pseudo_(pseudo),
tmp_(taus.size(), 0.0),
// zero initialization required for (used by) the last element
wkaj_(pseudo_.columns(), pseudo_.rows(), 0.0),
wkpj_(pseudo_.columns(), pseudo_.rows()+1, 0.0),
wkajshifted_(pseudo_.columns(), pseudo_.rows(), 0.0)
/*,
downs_(taus.size()), ups_(taus.size())*/ {
// Check requirements
QL_REQUIRE(numberOfRates_>0, "Dim out of range");
QL_REQUIRE(displacements.size() == numberOfRates_,
"Displacements 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 SMMDriftCalculator::compute(const CoterminalSwapCurveState& cs,
std::vector<Real>& drifts) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(drifts.size()==cs.numberOfRates(),
"drifts.size() <> numberOfRates");
#endif
// Compute drifts with factor reduction,
// using the pseudo square root of the covariance matrix.
const std::vector<Rate>& SR=cs.coterminalSwapRates();
// calculates and stores wkaj_, wkpj1_
// assuming terminal bond measure
// eq 5.4-5.7
const std::vector<Time>& taus=cs.rateTaus();
std::vector<Real> annuities(numberOfRates_);
for (Size j=0; j<numberOfRates_; ++j) {
annuities[j] = cs.coterminalSwapAnnuity(numberOfRates_, j);
}
for (Size k=0; k<numberOfFactors_; ++k) {
// taken care in the constructor
// wkpj1_[k][numberOfRates_-1]= 0.0;
// wkaj_[k][numberOfRates_-1] = 0.0;
for (Integer j=numberOfRates_-2; j>=static_cast<Integer>(alive_)-1; --j) {
// < W(k) | P(j+1)/P(n) > =
// = SR(j+1) a(j+1,k) A(j+1) / P(n) + SR(j+1) < W(k) | A(j+1)/P(n) >
Real annuity = annuities[j+1];
wkpj_[k][j+1]= SR[j+1] *
( pseudo_[j+1][k] * annuity + wkaj_[k][j+1] )+
pseudo_[j+1][k]*displacements_[j+1]* annuity;
if (j >=static_cast<Integer>(alive_))
wkaj_[k][j] = wkpj_[k][j+1]*taus[j ]+wkaj_[k][j+1];
}
}
Real numeraireRatio = cs.discountRatio(numberOfRates_, numeraire_);
// change to work for general numeraire
for (Size k=0; k<numberOfFactors_; ++k) {
// compute < Wk, PN/pn>
for (Size j=alive_; j<numberOfRates_; ++j)
{
wkajshifted_[k][j] = -wkaj_[k][j]/annuities[j]
+ wkpj_[k][numeraire_]
*numeraireRatio;
}
}
// eq 5.3 (in log coordinates)
for (Size j=alive_; j<numberOfRates_; ++j) {
drifts[j] = 0.0;
for (Size k=0; k<numberOfFactors_; ++k) {
drifts[j] += wkajshifted_[k][j]*pseudo_[j][k];
}
}
}
}
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