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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 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 fdmblackscholesmultistrikemesher.cpp
\brief 1-d mesher for the Black-Scholes process (in ln(S))
*/
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmultistrikemesher.hpp>
namespace QuantLib {
FdmBlackScholesMultiStrikeMesher::FdmBlackScholesMultiStrikeMesher(
Size size,
const boost::shared_ptr<GeneralizedBlackScholesProcess>& process,
Time maturity, const std::vector<Real>& strikes,
Real eps, Real scaleFactor,
const std::pair<Real, Real>& cPoint)
: Fdm1dMesher(size) {
const Real spot = process->x0();
QL_REQUIRE(spot > 0.0, "negative or null underlying given");
const DiscountFactor d = process->dividendYield()->discount(maturity)
/ process->riskFreeRate()->discount(maturity);
const Real minStrike= *std::min_element(strikes.begin(), strikes.end());
const Real maxStrike= *std::max_element(strikes.begin(), strikes.end());
const Real Fmin = spot*spot/maxStrike*d;
const Real Fmax = spot*spot/minStrike*d;
QL_REQUIRE(Fmin > 0.0, "negative forward given");
// Set the grid boundaries
const Real normInvEps = InverseCumulativeNormal()(1-eps);
const Real sigmaSqrtTmin
= process->blackVolatility()->blackVol(maturity, minStrike)
*std::sqrt(maturity);
const Real sigmaSqrtTmax
= process->blackVolatility()->blackVol(maturity, maxStrike)
*std::sqrt(maturity);
const Real xMin
= std::min(0.8*std::log(0.8*spot*spot/maxStrike),
std::log(Fmin) - sigmaSqrtTmin*normInvEps*scaleFactor
- sigmaSqrtTmin*sigmaSqrtTmin/2.0);
const Real xMax
= std::max(1.2*std::log(0.8*spot*spot/minStrike),
std::log(Fmax) + sigmaSqrtTmax*normInvEps*scaleFactor
- sigmaSqrtTmax*sigmaSqrtTmax/2.0);
boost::shared_ptr<Fdm1dMesher> helper;
if ( cPoint.first != Null<Real>()
&& std::log(cPoint.first) >=xMin && std::log(cPoint.first) <=xMax) {
helper = boost::shared_ptr<Fdm1dMesher>(
new Concentrating1dMesher(xMin, xMax, size,
std::pair<Real,Real>(std::log(cPoint.first),cPoint.second)));
}
else {
helper = boost::shared_ptr<Fdm1dMesher>(
new Uniform1dMesher(xMin, xMax, size));
}
locations_ = helper->locations();
for (Size i=0; i < locations_.size(); ++i) {
dplus_[i] = helper->dplus(i);
dminus_[i] = helper->dminus(i);
}
}
}
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