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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
<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 fdmblackscholesmesher.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/yield/quantotermstructure.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/methods/finitedifferences/utilities/fdmquantohelper.hpp>
#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmesher.hpp>
namespace QuantLib {
FdmBlackScholesMesher::FdmBlackScholesMesher(
Size size,
const ext::shared_ptr<GeneralizedBlackScholesProcess>& process,
Time maturity, Real strike,
Real xMinConstraint, Real xMaxConstraint,
Real eps, Real scaleFactor,
const std::pair<Real, Real>& cPoint,
const DividendSchedule& dividendSchedule,
const ext::shared_ptr<FdmQuantoHelper>& fdmQuantoHelper,
Real spotAdjustment)
: Fdm1dMesher(size) {
const Real S = process->x0();
QL_REQUIRE(S > 0.0, "negative or null underlying given");
std::vector<std::pair<Time, Real> > intermediateSteps;
for (const auto& i : dividendSchedule) {
const Time t = process->time(i->date());
if (t <= maturity && t >= 0.0)
intermediateSteps.emplace_back(process->time(i->date()), i->amount());
}
const Size intermediateTimeSteps = std::max<Size>(2, Size(24.0*maturity));
for (Size i=0; i < intermediateTimeSteps; ++i)
intermediateSteps.emplace_back((i + 1) * (maturity / intermediateTimeSteps), 0.0);
std::sort(intermediateSteps.begin(), intermediateSteps.end());
const Handle<YieldTermStructure> rTS = process->riskFreeRate();
const Handle<YieldTermStructure> qTS =
(fdmQuantoHelper) != nullptr ?
Handle<YieldTermStructure>(ext::make_shared<QuantoTermStructure>(
process->dividendYield(), process->riskFreeRate(),
Handle<YieldTermStructure>(fdmQuantoHelper->fTS_), process->blackVolatility(),
strike, Handle<BlackVolTermStructure>(fdmQuantoHelper->fxVolTS_),
fdmQuantoHelper->exchRateATMlevel_, fdmQuantoHelper->equityFxCorrelation_)) :
process->dividendYield();
Time lastDivTime = 0.0;
Real fwd = S + spotAdjustment;
Real mi = fwd, ma = fwd;
for (auto& intermediateStep : intermediateSteps) {
const Time divTime = intermediateStep.first;
const Real divAmount = intermediateStep.second;
fwd = fwd / rTS->discount(divTime) * rTS->discount(lastDivTime)
* qTS->discount(divTime) / qTS->discount(lastDivTime);
mi = std::min(mi, fwd); ma = std::max(ma, fwd);
fwd-= divAmount;
mi = std::min(mi, fwd); ma = std::max(ma, fwd);
lastDivTime = divTime;
}
// Set the grid boundaries
const Real normInvEps = InverseCumulativeNormal()(1-eps);
const Real sigmaSqrtT
= process->blackVolatility()->blackVol(maturity, strike)
*std::sqrt(maturity);
Real xMin = std::log(mi) - sigmaSqrtT*normInvEps*scaleFactor;
Real xMax = std::log(ma) + sigmaSqrtT*normInvEps*scaleFactor;
if (xMinConstraint != Null<Real>()) {
xMin = xMinConstraint;
}
if (xMaxConstraint != Null<Real>()) {
xMax = xMaxConstraint;
}
ext::shared_ptr<Fdm1dMesher> helper;
if ( cPoint.first != Null<Real>()
&& std::log(cPoint.first) >=xMin && std::log(cPoint.first) <=xMax) {
helper = ext::shared_ptr<Fdm1dMesher>(
new Concentrating1dMesher(xMin, xMax, size,
std::pair<Real,Real>(std::log(cPoint.first),
cPoint.second)));
}
else {
helper = ext::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);
}
}
ext::shared_ptr<GeneralizedBlackScholesProcess>
FdmBlackScholesMesher::processHelper(const Handle<Quote>& s0,
const Handle<YieldTermStructure>& rTS,
const Handle<YieldTermStructure>& qTS,
Volatility vol) {
return ext::make_shared<GeneralizedBlackScholesProcess>(
s0, qTS, rTS,
Handle<BlackVolTermStructure>(
ext::shared_ptr<BlackVolTermStructure>(
new BlackConstantVol(rTS->referenceDate(),
Calendar(),
vol,
rTS->dayCounter()))));
}
}
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