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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2018 Klaus Spanderen
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.
*/
/*! \file fdmsabrop.cpp
\brief FDM operator for the SABR model
*/
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/fdmsabrop.hpp>
#include <ql/methods/finitedifferences/operators/firstderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
namespace QuantLib {
FdmSabrOp::FdmSabrOp(const ext::shared_ptr<FdmMesher>& mesher,
ext::shared_ptr<YieldTermStructure> rTS,
Real f0,
Real alpha,
Real beta,
Real nu,
Real rho)
: rTS_(std::move(rTS)),
dffMap_(SecondDerivativeOp(0, mesher).mult(0.5 * Exp(2.0 * mesher->locations(1)) *
Pow(mesher->locations(0), 2.0 * beta))),
dxMap_(FirstDerivativeOp(1, mesher).mult(Array(mesher->layout()->size(), -0.5 * nu * nu))),
dxxMap_(SecondDerivativeOp(1, mesher).mult(Array(mesher->layout()->size(), 0.5 * nu * nu))),
correlationMap_(
SecondOrderMixedDerivativeOp(0, 1, mesher)
.mult(rho * nu * Exp(mesher->locations(1)) * Pow(mesher->locations(0), beta))),
mapF_(0, mesher), mapA_(1, mesher) {}
void FdmSabrOp::setTime(Time t1, Time t2) {
const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
mapF_.axpyb(Array(), dffMap_, dffMap_, Array(1, -0.5*r));
mapA_.axpyb(Array(1, 1.0), dxMap_, dxxMap_, Array(1, -0.5*r));
}
Size FdmSabrOp::size() const {
return 2;
}
Array FdmSabrOp::apply(const Array& u) const {
return mapF_.apply(u) + mapA_.apply(u) + correlationMap_.apply(u);
}
Array FdmSabrOp::apply_mixed(const Array& r) const {
return correlationMap_.apply(r);
}
Array FdmSabrOp::apply_direction(
Size direction, const Array& r) const {
if (direction == 0)
return mapF_.apply(r);
else if (direction == 1)
return mapA_.apply(r);
else
QL_FAIL("direction too large");
}
Array FdmSabrOp::solve_splitting(
Size direction, const Array& r, Real a) const {
if (direction == 0) {
return mapF_.solve_splitting(r, a, 1.0);
}
else if (direction == 1) {
return mapA_.solve_splitting(r, a, 1.0);
}
else
QL_FAIL("direction too large");
}
Array FdmSabrOp::preconditioner(
const Array& r, Real dt) const {
return solve_splitting(1, solve_splitting(0, r, dt), dt) ;
}
std::vector<SparseMatrix> FdmSabrOp::toMatrixDecomp() const {
return {
mapA_.toMatrix(),
mapF_.toMatrix(),
correlationMap_.toMatrix()
};
}
}
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