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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
<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.
*/
/*! \file fdmsabrop.cpp
\brief FDM operator for the SABR model
*/
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmsabrop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/firstderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
namespace QuantLib {
FdmSabrOp::FdmSabrOp(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<YieldTermStructure>& rTS,
Real f0, Real alpha, Real beta, Real nu, Real rho)
: rTS_ (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;
}
Disposable<Array> FdmSabrOp::apply(const Array& u) const {
return mapF_.apply(u) + mapA_.apply(u) + correlationMap_.apply(u);
}
Disposable<Array> FdmSabrOp::apply_mixed(const Array& r) const {
return correlationMap_.apply(r);
}
Disposable<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");
}
Disposable<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");
}
Disposable<Array> FdmSabrOp::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> > FdmSabrOp::toMatrixDecomp() const {
std::vector<SparseMatrix> retVal(3);
retVal[0] = mapA_.toMatrix();
retVal[1] = mapF_.toMatrix();
retVal[2] = correlationMap_.toMatrix();
return retVal;
}
#endif
}
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