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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Ferdinando Ametrano
Copyright (C) 2006 Marco Bianchetti
Copyright (C) 2006 Giorgio Facchinetti
Copyright (C) 2006, 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
<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/swapforwardmappings.hpp>
#include <ql/models/marketmodels/curvestate.hpp>
#include <ql/models/marketmodels/marketmodel.hpp>
#include <ql/models/marketmodels/evolutiondescription.hpp>
#include <ql/models/marketmodels/curvestates/lmmcurvestate.hpp>
#include <vector>
namespace QuantLib {
Real SwapForwardMappings::annuity(const CurveState& cs,
Size startIndex,
Size endIndex,
Size numeraireIndex)
{
Real annuity = 0.0;
for (Size i=startIndex; i<endIndex; ++i)
annuity += cs.rateTaus()[i]*cs.discountRatio(i+1, numeraireIndex);
return annuity;
}
// compute derivative of swap-rate to underlying forward rate
Real SwapForwardMappings::swapDerivative(const CurveState& cs,
Size startIndex,
Size endIndex,
Size forwardIndex)
{
if (forwardIndex < startIndex)
return 0.0;
if (forwardIndex >= endIndex)
return 0.0;
Real numerator = cs.discountRatio(startIndex, endIndex)-1;
Real swapAnnuity = annuity(cs, startIndex, endIndex,endIndex);
Real ratio = cs.rateTaus()[forwardIndex] /
(1 + cs.rateTaus()[forwardIndex] * cs.forwardRate(forwardIndex));
Real part1 = ratio*(numerator+1)/swapAnnuity;
Real part2 = numerator/(swapAnnuity*swapAnnuity);
if (forwardIndex >=1)
part2 *= ratio* annuity(cs, startIndex, forwardIndex, endIndex);
else
part2 = 0.0;
return part1-part2;
}
Disposable<Matrix>
SwapForwardMappings::coterminalSwapForwardJacobian(const CurveState& cs)
{
Size n = cs.numberOfRates();
const std::vector<Rate>& f = cs.forwardRates();
const std::vector<Time>& tau = cs.rateTaus();
// coterminal floating leg values
std::vector<Real> a(n);
for (Size k=0; k<n; ++k)
a[k] = cs.discountRatio(k,n)-1.0;
//p[k]-p[n];
Matrix jacobian = Matrix(n, n, 0.0);
for (Size i=0; i<n; ++i) { // i = swap rate index
for (Size j=i; j<n; ++j) { // j = forward rate index
Real bi = cs.coterminalSwapAnnuity(n,i);
Real bj = cs.coterminalSwapAnnuity(n,j);
jacobian[i][j] =
// p[j+1]*tau[j]/b[i] +
tau[j]/cs.coterminalSwapAnnuity(j+1,i) +
// tau[j]/(1.0+f[j]*tau[j]) *
tau[j]/(1.0+f[j]*tau[j]) *
// (-a[j]*b[i]+a[i]*b[j])/(b[i]*b[i]);
(-a[j]*bi+a[i]*bj)/(bi*bi);
}
}
return jacobian;
}
Disposable<Matrix>
SwapForwardMappings::coterminalSwapZedMatrix(const CurveState& cs,
const Spread displacement) {
Size n = cs.numberOfRates();
Matrix zMatrix = coterminalSwapForwardJacobian(cs);
const std::vector<Rate>& f = cs.forwardRates();
const std::vector<Rate>& sr = cs.coterminalSwapRates();
for (Size i=0; i<n; ++i)
for (Size j=i; j<n; ++j)
zMatrix[i][j] *= (f[j]+displacement)/(sr[i]+displacement);
return zMatrix;
}
Disposable<Matrix>
SwapForwardMappings::coinitialSwapForwardJacobian(const CurveState& cs)
{
Size n = cs.numberOfRates();
Matrix jacobian = Matrix(n, n, 0.0);
for (Size i=0; i<n; ++i) // i = swap rate index
for (Size j=0; j<n; ++j) // j = forward rate index
jacobian[i][j] =swapDerivative(cs, 0, i+1, j);
return jacobian;
}
Disposable<Matrix>
SwapForwardMappings::cmSwapForwardJacobian(const CurveState& cs,
const Size spanningForwards)
{
Size n = cs.numberOfRates();
Matrix jacobian = Matrix(n, n, 0.0);
for (Size i=0; i<n; ++i) // i = swap rate index
for (Size j=0; j<n; ++j) // j = forward rate index
jacobian[i][j] =swapDerivative(cs, i, std::min(n,i+spanningForwards), j);
return jacobian;
}
Disposable<Matrix>
SwapForwardMappings::coinitialSwapZedMatrix(const CurveState& cs,
const Spread displacement)
{
Size n = cs.numberOfRates();
Matrix zMatrix = coinitialSwapForwardJacobian(cs);
const std::vector<Rate>& f = cs.forwardRates();
std::vector<Rate> sr(n);
for (Size i=0; i<n; ++i)
sr[i] = cs.cmSwapRate(0,i+1);
for (Size i=0; i<n; ++i)
for (Size j=i; j<n; ++j)
zMatrix[i][j] *= (f[j]+displacement)/(sr[i]+displacement);
return zMatrix;
}
Disposable<Matrix>
SwapForwardMappings::cmSwapZedMatrix(const CurveState& cs,
const Size spanningForwards,
const Spread displacement)
{
Size n = cs.numberOfRates();
Matrix zMatrix = cmSwapForwardJacobian(cs,spanningForwards);
const std::vector<Rate>& f = cs.forwardRates();
std::vector<Rate> sr(n);
for (Size i=0; i<n; ++i)
sr[i] = cs.cmSwapRate(i,spanningForwards);
for (Size i=0; i<n; ++i)
for (Size j=i; j<n; ++j)
zMatrix[i][j] *= (f[j]+displacement)/(sr[i]+displacement);
return zMatrix;
}
Real
SwapForwardMappings::swaptionImpliedVolatility(const MarketModel& volStructure,
Size startIndex,
Size endIndex)
{
QL_REQUIRE(startIndex < endIndex, "start index must be before end index in swaptionImpliedVolatility");
LMMCurveState cs(volStructure.evolution().rateTimes());
cs.setOnForwardRates(volStructure.initialRates());
Real displacement = volStructure.displacements()[0];
Matrix cmsZed(cmSwapZedMatrix(cs, endIndex-startIndex,displacement));
Real variance=0.0;
Size index=0;
const EvolutionDescription& evolution(volStructure.evolution());
Size factors = volStructure.numberOfFactors();
while (index < evolution.numberOfSteps() && startIndex >= evolution.firstAliveRate()[index] )
{
const Matrix& thisPseudo = volStructure.pseudoRoot(index);
Real thisVariance =0.0;
for (Size f=0; f < factors; ++f)
{
Real sum=0.0;
for (Size j=startIndex; j < endIndex;++j)
{
sum += cmsZed[startIndex][j]*thisPseudo[j][f];
}
thisVariance += sum*sum;
}
variance += thisVariance;
++index;
}
Real expiry = evolution.rateTimes()[startIndex];
return std::sqrt(variance/expiry);
}
}
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