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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 Johannes Göttker-Schnetmann
Copyright (C) 2015 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 hestonslvmcmodel.cpp
*/
#include <ql/math/functional.hpp>
#include <ql/termstructures/volatility/equityfx/fixedlocalvolsurface.hpp>
#include <ql/experimental/models/hestonslvmcmodel.hpp>
#include <ql/experimental/processes/hestonslvprocess.hpp>
#if defined(__GNUC__) && (((__GNUC__ == 4) && (__GNUC_MINOR__ >= 8)) || (__GNUC__ > 4))
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
#endif
#include <boost/multi_array.hpp>
#if defined(__GNUC__) && (((__GNUC__ == 4) && (__GNUC_MINOR__ >= 8)) || (__GNUC__ > 4))
#pragma GCC diagnostic pop
#endif
namespace QuantLib {
HestonSLVMCModel::HestonSLVMCModel(
const Handle<LocalVolTermStructure>& localVol,
const Handle<HestonModel>& hestonModel,
const ext::shared_ptr<BrownianGeneratorFactory>& brownianGeneratorFactory,
const Date& endDate,
Size timeStepsPerYear,
Size nBins,
Size calibrationPaths,
const std::vector<Date>& mandatoryDates,
const Real mixingFactor)
: localVol_(localVol),
hestonModel_(hestonModel),
brownianGeneratorFactory_(brownianGeneratorFactory),
endDate_(endDate),
nBins_(nBins),
calibrationPaths_(calibrationPaths),
mixingFactor_(mixingFactor) {
registerWith(localVol_);
registerWith(hestonModel_);
const DayCounter dc = hestonModel_->process()->riskFreeRate()->dayCounter();
const Date refDate = hestonModel_->process()->riskFreeRate()->referenceDate();
std::vector<Time> gridTimes;
gridTimes.reserve(mandatoryDates.size()+1);
for (Size i=0; i < mandatoryDates.size(); ++i) {
gridTimes.push_back(dc.yearFraction(refDate, mandatoryDates[i]));
}
gridTimes.push_back(dc.yearFraction(refDate, endDate));
timeGrid_ = ext::make_shared<TimeGrid>(gridTimes.begin(), gridTimes.end(),
std::max(Size(2), Size(gridTimes.back()*timeStepsPerYear)));
}
ext::shared_ptr<HestonProcess> HestonSLVMCModel::hestonProcess() const {
return hestonModel_->process();
}
ext::shared_ptr<LocalVolTermStructure> HestonSLVMCModel::localVol() const {
return localVol_.currentLink();
}
ext::shared_ptr<LocalVolTermStructure>
HestonSLVMCModel::leverageFunction() const {
calculate();
return leverageFunction_;
}
void HestonSLVMCModel::performCalculations() const {
const ext::shared_ptr<HestonProcess> hestonProcess
= hestonModel_->process();
const ext::shared_ptr<Quote> spot
= hestonProcess->s0().currentLink();
const Real v0 = hestonProcess->v0();
const DayCounter dc = hestonProcess->riskFreeRate()->dayCounter();
const Date referenceDate = hestonProcess->riskFreeRate()->referenceDate();
const Volatility lv0
= localVol_->localVol(0.0, spot->value())/std::sqrt(v0);
const ext::shared_ptr<Matrix> L(new Matrix(nBins_, timeGrid_->size()));
std::vector<ext::shared_ptr<std::vector<Real> > >
vStrikes(timeGrid_->size());
for (Size i=0; i < timeGrid_->size(); ++i) {
const Integer u = nBins_/2;
const Real dx = spot->value()*std::sqrt(QL_EPSILON);
vStrikes[i] = ext::make_shared<std::vector<Real> >(nBins_);
for (Integer j=0; j < Integer(nBins_); ++j)
vStrikes[i]->at(j) = spot->value() + (j - u)*dx;
}
std::fill(L->column_begin(0),L->column_end(0), lv0);
leverageFunction_ = ext::make_shared<FixedLocalVolSurface>(
referenceDate,
std::vector<Time>(timeGrid_->begin(), timeGrid_->end()),
vStrikes, L, dc);
const ext::shared_ptr<HestonSLVProcess> slvProcess
= ext::make_shared<HestonSLVProcess>(hestonProcess, leverageFunction_, mixingFactor_);
std::vector<std::pair<Real, Real> > pairs(
calibrationPaths_, std::make_pair(spot->value(), v0));
const Size k = calibrationPaths_ / nBins_;
const Size m = calibrationPaths_ % nBins_;
const Size timeSteps = timeGrid_->size()-1;
typedef boost::multi_array<Real, 3> path_type;
path_type paths(boost::extents[calibrationPaths_][timeSteps][2]);
const ext::shared_ptr<BrownianGenerator> brownianGenerator =
brownianGeneratorFactory_->create(2, timeSteps);
for (Size i=0; i < calibrationPaths_; ++i) {
brownianGenerator->nextPath();
std::vector<Real> tmp(2);
for (Size j=0; j < timeSteps; ++j) {
brownianGenerator->nextStep(tmp);
paths[i][j][0] = tmp[0];
paths[i][j][1] = tmp[1];
}
}
for (Size n=1; n < timeGrid_->size(); ++n) {
const Time t = timeGrid_->at(n-1);
const Time dt = timeGrid_->dt(n-1);
Array x0(2), dw(2);
for (Size i=0; i < calibrationPaths_; ++i) {
x0[0] = pairs[i].first;
x0[1] = pairs[i].second;
dw[0] = paths[i][n-1][0];
dw[1] = paths[i][n-1][1];
x0 = slvProcess->evolve(t, x0, dt, dw);
pairs[i].first = x0[0];
pairs[i].second = x0[1];
}
std::sort(pairs.begin(), pairs.end());
Size s = 0U, e = 0U;
for (Size i=0; i < nBins_; ++i) {
const Size inc = k + static_cast<unsigned long>(i < m);
e = s + inc;
Real sum=0.0;
for (Size j=s; j < e; ++j) {
sum+=pairs[j].second;
}
sum/=inc;
vStrikes[n]->at(i) = 0.5*(pairs[e-1].first + pairs[s].first);
(*L)[i][n] = std::sqrt(square<Real>()(
localVol_->localVol(t, vStrikes[n]->at(i), true))/sum);
s = e;
}
leverageFunction_->setInterpolation<Linear>();
}
}
}
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