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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 Adrian O' Neill
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.
*/
#include <ql/exercise.hpp>
#include <ql/experimental/variancegamma/fftengine.hpp>
#include <ql/math/fastfouriertransform.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <complex>
#include <utility>
namespace QuantLib {
FFTEngine::FFTEngine(ext::shared_ptr<StochasticProcess1D> process, Real logStrikeSpacing)
: process_(std::move(process)), lambda_(logStrikeSpacing) {
registerWith(process_);
}
void FFTEngine::calculate() const
{
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"not an European Option");
ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-striked payoff given");
auto r1 = resultMap_.find(arguments_.exercise->lastDate());
if (r1 != resultMap_.end())
{
auto r2 = r1->second.find(payoff);
if (r2 != r1->second.end())
{
results_.value = r2->second;
return;
}
}
// Option not precalculated - do entire FFT for one option. Not very efficient - call precalculate!
calculateUncached(payoff, arguments_.exercise);
}
void FFTEngine::update()
{
// Process has changed so cached values may no longer be correct
resultMap_.clear();
// Call base class implementation
VanillaOption::engine::update();
}
void FFTEngine::calculateUncached(const ext::shared_ptr<StrikedTypePayoff>& payoff,
const ext::shared_ptr<Exercise>& exercise) const {
ext::shared_ptr<VanillaOption> option(new VanillaOption(payoff, exercise));
std::vector<ext::shared_ptr<Instrument> > optionList;
optionList.push_back(option);
ext::shared_ptr<FFTEngine> tempEngine(clone().release());
tempEngine->precalculate(optionList);
option->setPricingEngine(tempEngine);
results_.value = option->NPV();
}
void FFTEngine::precalculate(const std::vector<ext::shared_ptr<Instrument> >& optionList) {
// Group payoffs by expiry date
// as with FFT we can compute a bunch of these at once
resultMap_.clear();
typedef std::vector<ext::shared_ptr<StrikedTypePayoff> > PayoffList;
typedef std::map<Date, PayoffList> PayoffMap;
PayoffMap payoffMap;
for (const auto& optIt : optionList) {
ext::shared_ptr<VanillaOption> option = ext::dynamic_pointer_cast<VanillaOption>(optIt);
QL_REQUIRE(option, "instrument must be option");
QL_REQUIRE(option->exercise()->type() == Exercise::European,
"not an European Option");
ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(option->payoff());
QL_REQUIRE(payoff, "non-striked payoff given");
payoffMap[option->exercise()->lastDate()].push_back(payoff);
}
std::complex<Real> i1(0, 1);
Real alpha = 1.25;
for (auto & payIt : payoffMap)
{
Date expiryDate = payIt.first;
// Calculate n large enough for maximum strike, and round up to a power of 2
Real maxStrike = 0.0;
for (const auto& payoff : payIt.second) {
if (payoff->strike() > maxStrike)
maxStrike = payoff->strike();
}
Real nR = 2.0 * (std::log(maxStrike) + lambda_) / lambda_;
Size log2_n = (static_cast<Size>((std::log(nR) / std::log(2.0))) + 1);
Size n = static_cast<std::size_t>(1) << log2_n;
// Strike range (equation 19,20)
Real b = n * lambda_ / 2.0;
// Grid spacing (equation 23)
Real eta = 2.0 * M_PI / (lambda_ * n);
// Discount factor
Real df = discountFactor(expiryDate);
Real div = dividendYield(expiryDate);
// Input to fourier transform
std::vector<std::complex<Real> > fti;
fti.resize(n);
// Precalculate any discount factors etc.
precalculateExpiry(expiryDate);
for (Size i=0; i<n; i++)
{
Real v_j = eta * i;
Real sw = eta * (3.0 + ((i % 2) == 0 ? -1.0 : 1.0) - ((i == 0) ? 1.0 : 0.0)) / 3.0;
std::complex<Real> psi = df * complexFourierTransform(v_j - (alpha + 1)* i1);
psi = psi / (alpha*alpha + alpha - v_j*v_j + i1 * (2 * alpha + 1.0) * v_j);
fti[i] = std::exp(i1 * b * v_j) * sw * psi;
}
// Perform fft
std::vector<std::complex<Real> > results(n);
FastFourierTransform fft(log2_n);
fft.transform(fti.begin(), fti.end(), results.begin());
// Call prices
std::vector<Real> prices, strikes;
prices.resize(n);
strikes.resize(n);
for (Size i=0; i<n; i++)
{
Real k_u = -b + lambda_ * i;
prices[i] = (std::exp(-alpha * k_u) / M_PI) * results[i].real();
strikes[i] = std::exp(k_u);
}
for (const auto& payoff : payIt.second) {
Real callPrice = LinearInterpolation(strikes.begin(), strikes.end(),
prices.begin())(payoff->strike());
switch (payoff->optionType())
{
case Option::Call:
resultMap_[expiryDate][payoff] = callPrice;
break;
case Option::Put:
resultMap_[expiryDate][payoff] = callPrice - process_->x0() * div + payoff->strike() * df;
break;
default:
QL_FAIL("Invalid option type");
}
}
}
}
}
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