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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (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
<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/experimental/finitedifferences/fdmzabrop.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
namespace QuantLib {
FdmZabrUnderlyingPart::FdmZabrUnderlyingPart(
const ext::shared_ptr<FdmMesher> &mesher, const Real beta, const Real nu,
const Real rho, const Real gamma)
: volatilityValues_(mesher->locations(1)),
forwardValues_(mesher->locations(0)),
mapT_(SecondDerivativeOp(0, mesher)
.mult(0.5 * volatilityValues_ * volatilityValues_ *
Pow(forwardValues_, 2.0 * beta))),
mesher_(mesher) {}
void FdmZabrUnderlyingPart::setTime(Time t1, Time t2) {}
const TripleBandLinearOp &FdmZabrUnderlyingPart::getMap() const {
return mapT_;
}
FdmZabrVolatilityPart::FdmZabrVolatilityPart(
const ext::shared_ptr<FdmMesher> &mesher, const Real beta, const Real nu,
const Real rho, const Real gamma)
: volatilityValues_(mesher->locations(1)),
forwardValues_(mesher->locations(0)),
mapT_(SecondDerivativeOp(1, mesher).mult(
0.5 * nu * nu * Pow(volatilityValues_, 2.0 * gamma))),
mesher_(mesher) {}
void FdmZabrVolatilityPart::setTime(Time t1, Time t2) {}
const TripleBandLinearOp &FdmZabrVolatilityPart::getMap() const {
return mapT_;
}
FdmZabrOp::FdmZabrOp(const ext::shared_ptr<FdmMesher> &mesher,
const Real beta, const Real nu, const Real rho,
const Real gamma)
: volatilityValues_(mesher->locations(1)),
forwardValues_(mesher->locations(0)),
dxyMap_(SecondOrderMixedDerivativeOp(0, 1, mesher)
.mult(nu * rho * Pow(Abs(volatilityValues_), gamma + 1.0) *
Pow(forwardValues_, beta))),
dxMap_(FdmZabrUnderlyingPart(mesher, beta, nu, rho, gamma)),
dyMap_(FdmZabrVolatilityPart(mesher, beta, nu, rho, gamma)) {}
void FdmZabrOp::setTime(Time t1, Time t2) {
dxMap_.setTime(t1, t2);
dyMap_.setTime(t1, t2);
}
Size FdmZabrOp::size() const { return 2; }
Array FdmZabrOp::apply(const Array &u) const {
return dyMap_.getMap().apply(u) + dxMap_.getMap().apply(u) +
dxyMap_.apply(u);
}
Array FdmZabrOp::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");
}
Array FdmZabrOp::apply_mixed(const Array &r) const {
return dxyMap_.apply(r);
}
Array FdmZabrOp::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");
}
Array FdmZabrOp::preconditioner(const Array &r, Real dt) const {
return solve_splitting(0, r, dt);
}
std::vector<SparseMatrix> FdmZabrOp::toMatrixDecomp() const {
return {
dxMap_.getMap().toMatrix(),
dyMap_.getMap().toMatrix(),
dxyMap_.toMatrix()
};
}
}
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