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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012, 2013 Klaus Spanderen
Copyright (C) 2014 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
<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/math/functional.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/fdmblackscholesfwdop.hpp>
namespace QuantLib {
FdmBlackScholesFwdOp::FdmBlackScholesFwdOp(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<GeneralizedBlackScholesProcess> & bsProcess,
Real strike,
bool localVol,
Real illegalLocalVolOverwrite,
Size direction)
: mesher_(mesher),
rTS_ (bsProcess->riskFreeRate().currentLink()),
qTS_ (bsProcess->dividendYield().currentLink()),
volTS_ (bsProcess->blackVolatility().currentLink()),
localVol_((localVol) ? bsProcess->localVolatility().currentLink()
: ext::shared_ptr<LocalVolTermStructure>()),
x_ ((localVol) ? Array(Exp(mesher->locations(direction))) : Array()),
dxMap_ (FirstDerivativeOp(direction, mesher)),
dxxMap_(SecondDerivativeOp(direction, mesher)),
mapT_ (direction, mesher),
strike_(strike),
illegalLocalVolOverwrite_(illegalLocalVolOverwrite),
direction_(direction) {
}
void FdmBlackScholesFwdOp::setTime(Time t1, Time t2) {
const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
const Rate q = qTS_->forwardRate(t1, t2, Continuous).rate();
if (localVol_ != nullptr) {
Array v(mesher_->layout()->size());
for (const auto& iter : *mesher_->layout()) {
const Size i = iter.index();
if (illegalLocalVolOverwrite_ < 0.0) {
v[i] = squared(localVol_->localVol(0.5*(t1+t2), x_[i], true));
}
else {
try {
v[i] = squared(localVol_->localVol(0.5*(t1+t2), x_[i], true));
} catch (Error&) {
v[i] = squared(illegalLocalVolOverwrite_);
}
}
}
mapT_.axpyb(Array(1, 1.0), dxMap_.multR(- r + q + 0.5*v),
dxxMap_.multR(0.5*v), Array(1, 0.0));
} else {
const Real v
= volTS_->blackForwardVariance(t1, t2, strike_)/(t2-t1);
mapT_.axpyb(Array(1, - r + q + 0.5*v), dxMap_,
dxxMap_.mult(0.5*Array(mesher_->layout()->size(), v)),
Array(1, 0.0));
}
}
Size FdmBlackScholesFwdOp::size() const { return 1U; }
Array FdmBlackScholesFwdOp::apply(const Array& u) const {
return mapT_.apply(u);
}
Array FdmBlackScholesFwdOp::apply_direction(
Size direction, const Array& r) const {
if (direction == direction_)
return mapT_.apply(r);
else {
return Array(r.size(), 0.0);
}
}
Array FdmBlackScholesFwdOp::apply_mixed(const Array& r) const {
return Array(r.size(), 0.0);
}
Array FdmBlackScholesFwdOp::solve_splitting(
Size direction, const Array& r, Real dt) const {
if (direction == direction_)
return mapT_.solve_splitting(r, dt, 1.0);
else {
return r;
}
}
Array FdmBlackScholesFwdOp::preconditioner(
const Array& r, Real dt) const {
return solve_splitting(direction_, r, dt);
}
std::vector<SparseMatrix> FdmBlackScholesFwdOp::toMatrixDecomp() const {
return std::vector<SparseMatrix>(1, mapT_.toMatrix());
}
}
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