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|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Marco Bianchetti
Copyright (C) 2006, 2007 Giorgio Facchinetti
Cpoyright (C) 2014 Peter Caspers
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/termstructures/volatility/swaption/cmsmarketcalibration.hpp>
#include <ql/termstructures/volatility/swaption/cmsmarket.hpp>
#include <ql/termstructures/volatility/swaption/swaptionvolcube1.hpp>
#include <ql/math/optimization/problem.hpp>
#include <ql/math/optimization/constraint.hpp>
namespace {
using namespace QuantLib;
class ObjectiveFunction : public CostFunction {
public:
explicit ObjectiveFunction(CmsMarketCalibration *smileAndCms)
: smileAndCms_(smileAndCms), volCube_(smileAndCms->volCube_),
cmsMarket_(smileAndCms->cmsMarket_),
weights_(smileAndCms->weights_),
calibrationType_(smileAndCms->calibrationType_) {};
Real value(const Array& x) const override;
Array values(const Array& x) const override;
protected:
Real switchErrorFunctionOnCalibrationType() const;
Array switchErrorsFunctionOnCalibrationType() const;
CmsMarketCalibration *smileAndCms_;
Handle<SwaptionVolatilityStructure> volCube_;
ext::shared_ptr<CmsMarket> cmsMarket_;
Matrix weights_;
CmsMarketCalibration::CalibrationType calibrationType_;
private:
virtual void updateVolatilityCubeAndCmsMarket(const Array &x) const;
};
class ObjectiveFunction2 : public ObjectiveFunction {
public:
ObjectiveFunction2(CmsMarketCalibration *smileAndCms,
Real fixedMeanReversion)
: ObjectiveFunction(smileAndCms),
fixedMeanReversion_(fixedMeanReversion) {};
private:
void updateVolatilityCubeAndCmsMarket(const Array& x) const override;
Real fixedMeanReversion_;
};
class ObjectiveFunction3 : public ObjectiveFunction {
public:
explicit ObjectiveFunction3(CmsMarketCalibration *smileAndCms)
: ObjectiveFunction(smileAndCms) {};
private:
void updateVolatilityCubeAndCmsMarket(const Array& x) const override;
};
class ObjectiveFunction4 : public ObjectiveFunction {
public:
ObjectiveFunction4(CmsMarketCalibration *smileAndCms,
Real fixedMeanReversion)
: ObjectiveFunction(smileAndCms),
fixedMeanReversion_(fixedMeanReversion) {};
private:
void updateVolatilityCubeAndCmsMarket(const Array& x) const override;
Real fixedMeanReversion_;
};
class ObjectiveFunction5 : public ObjectiveFunction {
public:
ObjectiveFunction5(CmsMarketCalibration *smileAndCms,
Real fixedMeanReversion)
: ObjectiveFunction(smileAndCms),
fixedMeanReversion_(fixedMeanReversion) {};
private:
void updateVolatilityCubeAndCmsMarket(const Array& x) const override;
Real fixedMeanReversion_;
};
class ObjectiveFunction6 : public ObjectiveFunction {
public:
explicit ObjectiveFunction6(CmsMarketCalibration *smileAndCms)
: ObjectiveFunction(smileAndCms) {};
private:
void updateVolatilityCubeAndCmsMarket(const Array& x) const override;
};
//===========================================================================//
// ObjectiveFunction (constant beta, free mean reversion) //
//===========================================================================//
Real ObjectiveFunction::value(const Array &x) const {
updateVolatilityCubeAndCmsMarket(x);
return switchErrorFunctionOnCalibrationType();
}
Array ObjectiveFunction::values(const Array &x) const {
updateVolatilityCubeAndCmsMarket(x);
return switchErrorsFunctionOnCalibrationType();
}
void
ObjectiveFunction::updateVolatilityCubeAndCmsMarket(const Array &x) const {
const std::vector<Period> &swapTenors = cmsMarket_->swapTenors();
Size nSwapTenors = swapTenors.size();
QL_REQUIRE(nSwapTenors + 1 == x.size(),
"bad calibration guess nSwapTenors+1 != x.size()");
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
for (Size i = 0; i < nSwapTenors; ++i)
volCubeBySabr->recalibration(CmsMarketCalibration::betaTransformDirect(x[i]),
swapTenors[i]);
Real meanReversion =
CmsMarketCalibration::reversionTransformDirect(x[nSwapTenors]);
cmsMarket_->reprice(volCube_, meanReversion);
}
Real ObjectiveFunction::switchErrorFunctionOnCalibrationType() const {
switch (calibrationType_) {
case CmsMarketCalibration::OnSpread:
return cmsMarket_->weightedSpreadError(weights_);
case CmsMarketCalibration::OnPrice:
return cmsMarket_->weightedSpotNpvError(weights_);
case CmsMarketCalibration::OnForwardCmsPrice:
return cmsMarket_->weightedFwdNpvError(weights_);
default:
QL_FAIL("unknown/illegal calibration type");
}
}
Array ObjectiveFunction::switchErrorsFunctionOnCalibrationType() const {
switch (calibrationType_) {
case CmsMarketCalibration::OnSpread:
return cmsMarket_->weightedSpreadErrors(weights_);
case CmsMarketCalibration::OnPrice:
return cmsMarket_->weightedSpotNpvErrors(weights_);
case CmsMarketCalibration::OnForwardCmsPrice:
return cmsMarket_->weightedFwdNpvErrors(weights_);
default:
QL_FAIL("unknown/illegal calibration type");
}
}
//===========================================================================//
// ObjectiveFunction2 (constant beta, fixed mean reversion) //
//===========================================================================//
void
ObjectiveFunction2::updateVolatilityCubeAndCmsMarket(const Array &x) const {
const std::vector<Period> &swapTenors = cmsMarket_->swapTenors();
Size nSwapTenors = swapTenors.size();
QL_REQUIRE(nSwapTenors == x.size(),
"bad calibration guess nSwapTenors != x.size()");
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
for (Size i = 0; i < nSwapTenors; ++i)
volCubeBySabr->recalibration(QuantLib::CmsMarketCalibration::betaTransformDirect(x[i]),
swapTenors[i]);
cmsMarket_->reprice(volCube_, fixedMeanReversion_ == Null<Real>() ?
Null<Real>() :
QuantLib::CmsMarketCalibration::reversionTransformDirect(
fixedMeanReversion_));
}
//===========================================================================//
// ObjectiveFunction3 (beta termstructure, free mean reversion) //
//===========================================================================//
void
ObjectiveFunction3::updateVolatilityCubeAndCmsMarket(const Array &x) const {
const std::vector<Period> &swapTenors = cmsMarket_->swapTenors();
const std::vector<Period> &swapLengths = cmsMarket_->swapLengths();
Size nSwapTenors = swapTenors.size();
Size nSwapLengths = swapLengths.size();
QL_REQUIRE(
(nSwapLengths * nSwapTenors) + 1 == x.size(),
"bad calibration guess (nSwapLengths*nSwapTenors)+1 != x.size()");
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
for (Size i = 0; i < nSwapTenors; ++i) {
std::vector<Real> beta(x.begin() + (i * nSwapLengths),
x.begin() + ((i + 1) * nSwapLengths));
for (Real& j : beta)
j = CmsMarketCalibration::betaTransformDirect(j);
volCubeBySabr->recalibration(swapLengths, beta, swapTenors[i]);
}
Real meanReversion =
CmsMarketCalibration::reversionTransformDirect(x[nSwapLengths + nSwapTenors]);
cmsMarket_->reprice(volCube_, meanReversion);
}
//===========================================================================//
// ObjectiveFunction4 (beta termstructure, fixed mean reversion) //
//===========================================================================//
void
ObjectiveFunction4::updateVolatilityCubeAndCmsMarket(const Array &x) const {
const std::vector<Period> &swapTenors = cmsMarket_->swapTenors();
const std::vector<Period> &swapLengths = cmsMarket_->swapLengths();
Size nSwapTenors = swapTenors.size();
Size nSwapLengths = swapLengths.size();
QL_REQUIRE(
(nSwapLengths * nSwapTenors) == x.size(),
"bad calibration guess (nSwapLengths*nSwapTenors) != x.size()");
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
for (Size i = 0; i < nSwapTenors; ++i) {
std::vector<Real> beta(x.begin() + (i * nSwapLengths),
x.begin() + ((i + 1) * nSwapLengths));
for (Real& j : beta)
j = CmsMarketCalibration::betaTransformDirect(j);
volCubeBySabr->recalibration(swapLengths, beta, swapTenors[i]);
}
cmsMarket_->reprice(volCube_, fixedMeanReversion_ == Null<Real>() ?
Null<Real>() :
CmsMarketCalibration::reversionTransformDirect(
fixedMeanReversion_));
}
//=============================================================================//
// ObjectiveFunction5 (beta parameteric termstructure, fixed mean reversion) //
//=============================================================================//
void
ObjectiveFunction5::updateVolatilityCubeAndCmsMarket(const Array &x) const {
const std::vector<Period> &swapTenors = cmsMarket_->swapTenors();
const std::vector<Period> &swapLengths = cmsMarket_->swapLengths();
Size nSwapTenors = swapTenors.size();
Size nSwapLengths = swapLengths.size();
QL_REQUIRE((3 * nSwapTenors) == x.size(),
"bad calibration guess (3*nSwapTenors) != x.size()");
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
for (Size i = 0; i < nSwapTenors; ++i) {
Real betaInf = CmsMarketCalibration::betaTransformDirect(x[0 + 3 * i]);
Real beta0 = CmsMarketCalibration::betaTransformDirect(x[1 + 3 * i]);
Real decay = x[2 + 3 * i] * x[2 + 3 * i];
std::vector<Real> beta(nSwapLengths);
for (Size j = 0; j < beta.size(); ++j) {
Real t = smileAndCms_->volCube_->timeFromReference(
smileAndCms_->volCube_->optionDateFromTenor(swapLengths[j]));
beta[j] = betaInf + (beta0 - betaInf) * std::exp(-decay * t);
}
volCubeBySabr->recalibration(swapLengths, beta, swapTenors[i]);
}
cmsMarket_->reprice(volCube_, fixedMeanReversion_ == Null<Real>() ?
Null<Real>() :
CmsMarketCalibration::reversionTransformDirect(
fixedMeanReversion_));
}
//===========================================================================//
// ObjectiveFunction6 (beta parameteric termstructure, free mean reversion) //
//===========================================================================//
void
ObjectiveFunction6::updateVolatilityCubeAndCmsMarket(const Array &x) const {
const std::vector<Period> &swapTenors = cmsMarket_->swapTenors();
const std::vector<Period> &swapLengths = cmsMarket_->swapLengths();
Size nSwapTenors = swapTenors.size();
Size nSwapLengths = swapLengths.size();
QL_REQUIRE((3 * nSwapTenors) == x.size(),
"bad calibration guess (3*nSwapTenors) != x.size()");
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
for (Size i = 0; i < nSwapTenors; ++i) {
Real betaInf = CmsMarketCalibration::betaTransformDirect(x[0 + 3 * i]);
Real beta0 = CmsMarketCalibration::betaTransformDirect(x[1 + 3 * i]);
Real decay = x[2 + 3 * i] * x[2 + 3 * i];
std::vector<Real> beta(nSwapLengths);
for (Size j = 0; j < beta.size(); ++j) {
Real t = smileAndCms_->volCube_->timeFromReference(
smileAndCms_->volCube_->optionDateFromTenor(swapLengths[j]));
beta[j] = betaInf + (beta0 - betaInf) * std::exp(-decay * t);
}
volCubeBySabr->recalibration(swapLengths, beta, swapTenors[i]);
}
Real meanReversion =
CmsMarketCalibration::reversionTransformDirect(x[3 * nSwapTenors]);
cmsMarket_->reprice(volCube_, meanReversion);
}
}
namespace QuantLib {
//===========================================================================//
// CmsMarketCalibration //
//===========================================================================//
CmsMarketCalibration::CmsMarketCalibration(
Handle<SwaptionVolatilityStructure> &volCube,
ext::shared_ptr<CmsMarket> &cmsMarket, const Matrix &weights,
CalibrationType calibrationType)
: volCube_(volCube), cmsMarket_(cmsMarket), weights_(weights),
calibrationType_(calibrationType) {
QL_REQUIRE(weights.rows() == cmsMarket_->swapLengths().size(),
"weights number of rows ("
<< weights.rows()
<< ") must be equal to number of swap lengths ("
<< cmsMarket_->swapLengths().size() << ")");
QL_REQUIRE(weights.columns() == cmsMarket_->swapTenors().size(),
"weights number of columns ("
<< weights.columns()
<< ") must be equal to number of swap indexes ("
<< cmsMarket_->swapTenors().size());
}
Array CmsMarketCalibration::compute(
const ext::shared_ptr<EndCriteria> &endCriteria,
const ext::shared_ptr<OptimizationMethod> &method, const Array &guess,
bool isMeanReversionFixed) {
Size nSwapTenors = cmsMarket_->swapTenors().size();
QL_REQUIRE(isMeanReversionFixed || guess.size() == nSwapTenors + 1,
"if mean reversion is not fixed, a guess must be provided");
QL_REQUIRE(nSwapTenors == guess.size() ||
nSwapTenors == guess.size() - 1,
"guess size (" << guess.size()
<< ") must be equal to swap tenors size ("
<< nSwapTenors
<< ") or greater by one if mean reversion is "
"given as last element");
bool isMeanReversionGiven = (nSwapTenors == guess.size() - 1);
Size nBeta = guess.size() - (isMeanReversionGiven ? 1 : 0);
Array result;
if (isMeanReversionFixed) {
NoConstraint constraint;
Real fixedMeanReversion =
isMeanReversionGiven ? guess[nBeta] : Null<Real>();
Array betasGuess(nBeta);
for (Size i = 0; i < nBeta; ++i)
betasGuess[i] = guess[i];
ObjectiveFunction2 costFunction(
this, fixedMeanReversion == Null<Real>()
? Null<Real>()
: reversionTransformInverse(fixedMeanReversion));
Problem problem(costFunction, constraint, betasGuess);
endCriteria_ = method->minimize(problem, *endCriteria);
Array tmp = problem.currentValue();
error_ = costFunction.value(tmp);
result = Array(nBeta + (isMeanReversionGiven ? 1 : 0));
for (Size i = 0; i < nBeta; ++i)
result[i] = betaTransformDirect(tmp[i]);
if (isMeanReversionGiven)
result[nBeta] = fixedMeanReversion;
} else {
NoConstraint constraint;
ObjectiveFunction costFunction(this);
Array betaReversionGuess(nBeta + 1);
for (Size i = 0; i < nBeta; ++i)
betaReversionGuess[i] = betaTransformInverse(guess[i]);
betaReversionGuess[nBeta] = reversionTransformInverse(guess[nBeta]);
Problem problem(costFunction, constraint, betaReversionGuess);
endCriteria_ = method->minimize(problem, *endCriteria);
result = problem.currentValue();
error_ = costFunction.value(result);
for (Size i = 0; i < nBeta; ++i)
result[i] = betaTransformDirect(result[i]);
result[nBeta] = reversionTransformDirect(result[nBeta]);
}
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
volCubeBySabr->updateAfterRecalibration();
sparseSabrParameters_ = volCubeBySabr->sparseSabrParameters();
denseSabrParameters_ = volCubeBySabr->denseSabrParameters();
browseCmsMarket_ = cmsMarket_->browse();
return result;
}
Matrix CmsMarketCalibration::compute(
const ext::shared_ptr<EndCriteria> &endCriteria,
const ext::shared_ptr<OptimizationMethod> &method,
const Matrix &guess, bool isMeanReversionFixed,
const Real meanReversionGuess) {
Size nSwapTenors = cmsMarket_->swapTenors().size();
Size nSwapLengths = cmsMarket_->swapLengths().size();
QL_REQUIRE(isMeanReversionFixed || meanReversionGuess != Null<Real>(),
"if mean reversion is not fixed, a guess must be provided");
QL_REQUIRE(nSwapTenors == guess.columns(),
"number of swap tenors ("
<< nSwapTenors
<< ") must be equal to number of guess columns ("
<< guess.columns() << ")");
QL_REQUIRE(nSwapLengths == guess.rows(),
"number of swap lengths ("
<< nSwapLengths
<< ") must be equal to number of guess rows ("
<< guess.rows() << ")");
Matrix result;
Size nBeta = nSwapTenors * nSwapLengths;
if (isMeanReversionFixed) {
NoConstraint constraint;
Array betasGuess(nBeta);
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < nSwapLengths; ++j) {
betasGuess[i * nSwapLengths + j] =
betaTransformInverse(guess[j][i]);
}
}
ObjectiveFunction4 costFunction(
this, meanReversionGuess == Null<Real>()
? meanReversionGuess
: reversionTransformInverse(meanReversionGuess));
Problem problem(costFunction, constraint, betasGuess);
endCriteria_ = method->minimize(problem, *endCriteria);
Array tmp = problem.currentValue();
error_ = costFunction.value(tmp);
result = Matrix(nSwapLengths,
nSwapTenors +
(meanReversionGuess != Null<Real>() ? 1 : 0));
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < nSwapLengths; ++j) {
result[j][i] =
betaTransformDirect(tmp[i * nSwapLengths + j]);
}
}
if (meanReversionGuess != Null<Real>()) {
for (Size j = 0; j < nSwapLengths; ++j) {
result[j][nSwapTenors] = meanReversionGuess;
}
}
} else {
NoConstraint constraint;
Array betasReversionGuess(nBeta + 1);
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < nSwapLengths; ++j) {
betasReversionGuess[i * nSwapLengths + j] =
betaTransformInverse(guess[j][i]);
}
}
betasReversionGuess[nBeta] =
reversionTransformInverse(meanReversionGuess);
ObjectiveFunction3 costFunction(this);
Problem problem(costFunction, constraint, betasReversionGuess);
endCriteria_ = method->minimize(problem, *endCriteria);
Array tmp = problem.currentValue();
error_ = costFunction.value(tmp);
result = Matrix(nSwapLengths, nSwapTenors + 1);
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < nSwapLengths; ++j) {
result[j][i] =
betaTransformDirect(tmp[i * nSwapLengths + j]);
}
}
for (Size j = 0; j < nSwapLengths; ++j) {
result[j][nSwapTenors] = reversionTransformDirect(tmp[nBeta]);
}
}
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
volCubeBySabr->updateAfterRecalibration();
sparseSabrParameters_ = volCubeBySabr->sparseSabrParameters();
denseSabrParameters_ = volCubeBySabr->denseSabrParameters();
browseCmsMarket_ = cmsMarket_->browse();
return result;
}
Matrix CmsMarketCalibration::computeParametric(
const ext::shared_ptr<EndCriteria> &endCriteria,
const ext::shared_ptr<OptimizationMethod> &method,
const Matrix &guess, bool isMeanReversionFixed,
const Real meanReversionGuess) {
Size nSwapTenors = cmsMarket_->swapTenors().size();
Size nSwapLengths = cmsMarket_->swapLengths().size();
QL_REQUIRE(isMeanReversionFixed || meanReversionGuess != Null<Real>(),
"if mean reversion is not fixed, a guess must be provided");
QL_REQUIRE(nSwapTenors == guess.columns(),
"number of swap tenors ("
<< nSwapTenors
<< ") must be equal to number of guess columns ("
<< guess.columns() << ")");
QL_REQUIRE(3 == guess.rows(),
"number of parameters ("
<< 3 << ") must be equal to number of guess rows ("
<< guess.rows() << ")");
Matrix result;
Size nParams = nSwapTenors * 3;
if (isMeanReversionFixed) {
NoConstraint constraint;
Array betasGuess(nParams);
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < nParams; ++j) {
betasGuess[i * 3 + j] =
(j == 0 || j == 1) ? betaTransformInverse(guess[j][i])
: std::sqrt(guess[j][i]);
}
}
ObjectiveFunction5 costFunction(
this, meanReversionGuess == Null<Real>()
? meanReversionGuess
: reversionTransformInverse(meanReversionGuess));
Problem problem(costFunction, constraint, betasGuess);
endCriteria_ = method->minimize(problem, *endCriteria);
Array tmp = problem.currentValue();
error_ = costFunction.value(tmp);
result = Matrix(
3, nSwapTenors + (meanReversionGuess != Null<Real>() ? 1 : 0));
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < 3; ++j) {
result[j][i] = (j == 0 || j == 1)
? betaTransformDirect(tmp[i * 3 + j])
: tmp[i * 3 + j] * tmp[i * 3 + j];
}
}
if (meanReversionGuess != Null<Real>()) {
for (Size j = 0; j < nSwapLengths; ++j) {
result[j][nSwapTenors] = meanReversionGuess;
}
}
} else {
NoConstraint constraint;
Array betasReversionGuess(nParams + 1);
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < nParams; ++j) {
betasReversionGuess[i * nSwapLengths + j] =
(j == 0 || j == 1) ? betaTransformInverse(guess[j][i])
: std::sqrt(guess[j][i]);
}
}
betasReversionGuess[nParams] =
reversionTransformInverse(meanReversionGuess);
ObjectiveFunction6 costFunction(this);
Problem problem(costFunction, constraint, betasReversionGuess);
endCriteria_ = method->minimize(problem, *endCriteria);
Array tmp = problem.currentValue();
error_ = costFunction.value(tmp);
result = Matrix(3, nSwapTenors + 1);
for (Size i = 0; i < nSwapTenors; ++i) {
for (Size j = 0; j < 3; ++j) {
result[j][i] =
(j == 0 || j == 1)
? betaTransformDirect(tmp[i * nSwapLengths + j])
: tmp[i * 3 + j] * tmp[i * 3 + j];
}
}
for (Size j = 0; j < nSwapLengths; ++j) {
result[j][nSwapTenors] = reversionTransformDirect(tmp[nParams]);
}
}
const ext::shared_ptr<SwaptionVolCube1> volCubeBySabr =
ext::dynamic_pointer_cast<SwaptionVolCube1>(*volCube_);
volCubeBySabr->updateAfterRecalibration();
sparseSabrParameters_ = volCubeBySabr->sparseSabrParameters();
denseSabrParameters_ = volCubeBySabr->denseSabrParameters();
browseCmsMarket_ = cmsMarket_->browse();
return result;
}
}
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