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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Andreas Gaida
Copyright (C) 2008 Ralph Schreyer
Copyright (C) 2008, 2014, 2015 Klaus Spanderen
Copyright (C) 2015 Johannes Göttker-Schnetmann
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/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmhestonop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
namespace QuantLib {
FdmHestonEquityPart::FdmHestonEquityPart(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<YieldTermStructure>& rTS,
const ext::shared_ptr<YieldTermStructure>& qTS,
const ext::shared_ptr<FdmQuantoHelper>& quantoHelper,
const ext::shared_ptr<LocalVolTermStructure>& leverageFct)
: varianceValues_(0.5*mesher->locations(1)),
dxMap_ (FirstDerivativeOp(0, mesher)),
dxxMap_(SecondDerivativeOp(0, mesher).mult(0.5*mesher->locations(1))),
mapT_ (0, mesher),
mesher_(mesher),
rTS_(rTS),
qTS_(qTS),
quantoHelper_(quantoHelper),
leverageFct_(leverageFct) {
// on the boundary s_min and s_max the second derivative
// d^2V/dS^2 is zero and due to Ito's Lemma the variance term
// in the drift should vanish.
ext::shared_ptr<FdmLinearOpLayout> layout = mesher_->layout();
FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
if ( iter.coordinates()[0] == 0
|| iter.coordinates()[0] == layout->dim()[0]-1) {
varianceValues_[iter.index()] = 0.0;
}
}
volatilityValues_ = Sqrt(2*varianceValues_);
}
void FdmHestonEquityPart::setTime(Time t1, Time t2) {
const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
const Rate q = qTS_->forwardRate(t1, t2, Continuous).rate();
L_ = getLeverageFctSlice(t1, t2);
const Array Lsquare = L_*L_;
if (quantoHelper_ != 0) {
mapT_.axpyb(r - q - varianceValues_*Lsquare
- quantoHelper_->quantoAdjustment(
volatilityValues_*L_, t1, t2),
dxMap_, dxxMap_.mult(Lsquare), Array(1, -0.5*r));
}
else {
mapT_.axpyb(r - q - varianceValues_*Lsquare, dxMap_,
dxxMap_.mult(Lsquare), Array(1, -0.5*r));
}
}
Disposable<Array> FdmHestonEquityPart::getLeverageFctSlice(Time t1, Time t2)
const {
const ext::shared_ptr<FdmLinearOpLayout> layout=mesher_->layout();
Array v(layout->size(), 1.0);
if (!leverageFct_) {
return v;
}
const Real t = 0.5*(t1+t2);
const Time time = std::min(leverageFct_->maxTime(), t);
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin();
iter!=endIter; ++iter) {
const Size nx = iter.coordinates()[0];
if (iter.coordinates()[1] == 0) {
const Real x = std::exp(mesher_->location(iter, 0));
const Real spot = std::min(leverageFct_->maxStrike(),
std::max(leverageFct_->minStrike(), x));
v[nx] = std::max(0.01, leverageFct_->localVol(time, spot, true));
}
else {
v[iter.index()] = v[nx];
}
}
return v;
}
const TripleBandLinearOp& FdmHestonEquityPart::getMap() const {
return mapT_;
}
FdmHestonVariancePart::FdmHestonVariancePart(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<YieldTermStructure>& rTS,
Real mixedSigma, Real kappa, Real theta)
: dyMap_(SecondDerivativeOp(1, mesher)
.mult(0.5*mixedSigma*mixedSigma*mesher->locations(1))
.add(FirstDerivativeOp(1, mesher)
.mult(kappa*(theta - mesher->locations(1))))),
mapT_(1, mesher),
rTS_(rTS) {
}
void FdmHestonVariancePart::setTime(Time t1, Time t2) {
const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
mapT_.axpyb(Array(), dyMap_, dyMap_, Array(1,-0.5*r));
}
const TripleBandLinearOp& FdmHestonVariancePart::getMap() const {
return mapT_;
}
FdmHestonOp::FdmHestonOp(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<HestonProcess> & hestonProcess,
const ext::shared_ptr<FdmQuantoHelper>& quantoHelper,
const ext::shared_ptr<LocalVolTermStructure>& leverageFct,
const Real mixingFactor)
: correlationMap_(SecondOrderMixedDerivativeOp(0, 1, mesher)
.mult(hestonProcess->rho()*hestonProcess->sigma()
*mixingFactor
*mesher->locations(1))),
dyMap_(mesher, hestonProcess->riskFreeRate().currentLink(),
hestonProcess->sigma()*mixingFactor,
hestonProcess->kappa(),
hestonProcess->theta()),
dxMap_(mesher,
hestonProcess->riskFreeRate().currentLink(),
hestonProcess->dividendYield().currentLink(),
quantoHelper, leverageFct) {
}
void FdmHestonOp::setTime(Time t1, Time t2) {
dxMap_.setTime(t1, t2);
dyMap_.setTime(t1, t2);
}
Size FdmHestonOp::size() const {
return 2;
}
Disposable<Array> FdmHestonOp::apply(const Array& u) const {
return dyMap_.getMap().apply(u) + dxMap_.getMap().apply(u)
+ dxMap_.getL()*correlationMap_.apply(u);
}
Disposable<Array> FdmHestonOp::apply_direction(Size direction,
const Array& r) const {
if (direction == 0)
return dxMap_.getMap().apply(r);
else if (direction == 1)
return dyMap_.getMap().apply(r);
else
QL_FAIL("direction too large");
}
Disposable<Array> FdmHestonOp::apply_mixed(const Array& r) const {
return dxMap_.getL()*correlationMap_.apply(r);
}
Disposable<Array>
FdmHestonOp::solve_splitting(Size direction,
const Array& r, Real a) const {
if (direction == 0) {
return dxMap_.getMap().solve_splitting(r, a, 1.0);
}
else if (direction == 1) {
return dyMap_.getMap().solve_splitting(r, a, 1.0);
}
else
QL_FAIL("direction too large");
}
Disposable<Array>
FdmHestonOp::preconditioner(const Array& r, Real dt) const {
return solve_splitting(1, solve_splitting(0, r, dt), dt) ;
}
#if !defined(QL_NO_UBLAS_SUPPORT)
Disposable<std::vector<SparseMatrix> >
FdmHestonOp::toMatrixDecomp() const {
std::vector<SparseMatrix> retVal(3);
retVal[0] = dxMap_.getMap().toMatrix();
retVal[1] = dyMap_.getMap().toMatrix();
retVal[2] = correlationMap_.toMatrix();
return retVal;
}
#endif
}
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