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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 Adrian O' Neill
Copyright (C) 2018 Roy Zywina
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.
*/
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/instruments/europeanoption.hpp>
#include <ql/experimental/variancegamma/analyticvariancegammaengine.hpp>
#include <ql/experimental/variancegamma/fftvariancegammaengine.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <map>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(VarianceGammaTests)
#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoff, exercise, s, q, r, today, sigma, \
nu, theta, expected, calculated, \
error, tolerance) \
BOOST_FAIL(exerciseTypeToString(exercise) << " " \
<< payoff->optionType() << " option with " \
<< payoffTypeToString(payoff) << " payoff:\n" \
<< " underlying value: " << s << "\n" \
<< " strike: " << payoff->strike() <<"\n" \
<< " dividend yield: " << io::rate(q) << "\n" \
<< " risk-free rate: " << io::rate(r) << "\n" \
<< " reference date: " << today << "\n" \
<< " maturity: " << exercise->lastDate() << "\n" \
<< " sigma: " << sigma << "\n" \
<< " nu: " << nu << "\n" \
<< " theta: " << theta << "\n\n" \
<< " expected " << greekName << ": " << expected << "\n" \
<< " calculated " << greekName << ": " << calculated << "\n"\
<< " error: " << error << "\n" \
<< " tolerance: " << tolerance);
struct VarianceGammaProcessData {
Real s; // spot
Rate q; // dividend
Rate r; // risk-free rate
Real sigma;
Real nu;
Real theta;
};
struct VarianceGammaOptionData {
Option::Type type;
Real strike;
Time t; // time to maturity
};
BOOST_AUTO_TEST_CASE(testVarianceGamma) {
BOOST_TEST_MESSAGE("Testing variance-gamma model for European options...");
VarianceGammaProcessData processes[] = {
// spot, q, r,sigma, nu, theta
{ 6000, 0.00, 0.05, 0.20, 0.05, -0.50 },
{ 6000, 0.02, 0.05, 0.15, 0.01, -0.50 }
};
VarianceGammaOptionData options[] = {
// type,strike, t
{ Option::Call, 5550, 1.0},
{ Option::Call, 5600, 1.0},
{ Option::Call, 5650, 1.0},
{ Option::Call, 5700, 1.0},
{ Option::Call, 5750, 1.0},
{ Option::Call, 5800, 1.0},
{ Option::Call, 5850, 1.0},
{ Option::Call, 5900, 1.0},
{ Option::Call, 5950, 1.0},
{ Option::Call, 6000, 1.0},
{ Option::Call, 6050, 1.0},
{ Option::Call, 6100, 1.0},
{ Option::Call, 6150, 1.0},
{ Option::Call, 6200, 1.0},
{ Option::Call, 6250, 1.0},
{ Option::Call, 6300, 1.0},
{ Option::Call, 6350, 1.0},
{ Option::Call, 6400, 1.0},
{ Option::Call, 6450, 1.0},
{ Option::Call, 6500, 1.0},
{ Option::Call, 6550, 1.0},
{ Option::Put, 5550, 1.0}
};
Real results[std::size(processes)][std::size(options)] = {
{
955.1637, 922.7529, 890.9872, 859.8739, 829.4197, 799.6303, 770.5104, 742.0640,
714.2943, 687.2032, 660.7921, 635.0613, 610.0103, 585.6379, 561.9416, 538.9186,
516.5649, 494.8760, 473.8464, 453.4700, 433.7400, 234.4870
},
{
732.8705, 698.5542, 665.1404, 632.6498, 601.1002, 570.5068, 540.8824, 512.2367,
484.5766, 457.9064, 432.2273, 407.5381, 383.8346, 361.1102, 339.3559, 318.5599,
298.7087, 279.7864, 261.7751, 244.6552, 228.4057, 130.9974
}
};
Real tol = 0.01;
DayCounter dc = Actual360();
Date today = Date::todaysDate();
for (Size i=0; i<std::size(processes); i++) {
ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(processes[i].s));
ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(processes[i].q));
ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(processes[i].r));
ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
ext::shared_ptr<VarianceGammaProcess> stochProcess(
new VarianceGammaProcess(Handle<Quote>(spot),
Handle<YieldTermStructure>(qTS),
Handle<YieldTermStructure>(rTS),
processes[i].sigma,
processes[i].nu,
processes[i].theta));
// Analytic engine
ext::shared_ptr<PricingEngine> analyticEngine(
new VarianceGammaEngine(stochProcess));
// FFT engine
ext::shared_ptr<FFTVarianceGammaEngine> fftEngine(
new FFTVarianceGammaEngine(stochProcess));
// which requires a list of options
std::vector<ext::shared_ptr<Instrument> > optionList;
std::vector<ext::shared_ptr<StrikedTypePayoff> > payoffs;
for (Size j=0; j<std::size(options); j++)
{
Date exDate = today + timeToDays(options[j].t);
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
ext::shared_ptr<StrikedTypePayoff> payoff(new
PlainVanillaPayoff(options[j].type, options[j].strike));
payoffs.push_back(payoff);
// Test analytic engine
ext::shared_ptr<EuropeanOption> option(new EuropeanOption(payoff, exercise));
option->setPricingEngine(analyticEngine);
Real calculated = option->NPV();
Real expected = results[i][j];
Real error = std::fabs(calculated-expected);
if (error>tol) {
REPORT_FAILURE("analytic value", payoff, exercise,
processes[i].s, processes[i].q, processes[i].r,
today, processes[i].sigma, processes[i].nu,
processes[i].theta, expected, calculated,
error, tol);
}
optionList.push_back(option);
}
// Test FFT engine
// FFT engine is extremely efficient when sent a list of options to calculate first
fftEngine->precalculate(optionList);
for (Size j=0; j<std::size(options); j++)
{
ext::shared_ptr<VanillaOption> option = ext::static_pointer_cast<VanillaOption>(optionList[j]);
option->setPricingEngine(fftEngine);
Real calculated = option->NPV();
Real expected = results[i][j];
Real error = std::fabs(calculated-expected);
if (error>tol) {
ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(option->payoff());
REPORT_FAILURE("fft value", payoff, option->exercise(),
processes[i].s, processes[i].q, processes[i].r,
today, processes[i].sigma, processes[i].nu,
processes[i].theta, expected, calculated,
error, tol);
}
}
}
}
BOOST_AUTO_TEST_CASE(testSingularityAtZero) {
BOOST_TEST_MESSAGE(
"Testing variance-gamma model integration around zero...");
Real stock = 100;
Real strike = 98;
Volatility sigma = 0.12;
Real mu = -0.14;
Real kappa = 0.2;
Date valuation(1,Jan,2017);
Date maturity(10,Jan,2017);
DayCounter discountCounter = Thirty360(Thirty360::BondBasis);
Settings::instance().evaluationDate() = valuation;
ext::shared_ptr<Exercise> exercise =
ext::make_shared<EuropeanExercise>(maturity);
ext::shared_ptr<StrikedTypePayoff> payoff =
ext::make_shared<PlainVanillaPayoff>(Option::Call, strike);
VanillaOption option(payoff, exercise);
Handle<YieldTermStructure> dividend(
ext::make_shared<FlatForward>(valuation,0.0,discountCounter));
Handle<YieldTermStructure> disc(
ext::make_shared<FlatForward>(valuation,0.05,discountCounter));
Handle<Quote> S0(ext::make_shared<SimpleQuote>(stock));
ext::shared_ptr<QuantLib::VarianceGammaProcess> process =
ext::make_shared<VarianceGammaProcess>(S0, dividend, disc,
sigma, kappa, mu);
option.setPricingEngine(ext::make_shared<VarianceGammaEngine>(process));
// without the fix, the call below goes into an infinite loop,
// which is hard to test for. We're just happy to see the test
// case finish, hence the lack of an assertion.
option.NPV();
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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