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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2005, 2008 Klaus Spanderen
Copyright (C) 2007 StatPro Italia srl
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/calendars/target.hpp>
#include <ql/processes/batesprocess.hpp>
#include <ql/processes/merton76process.hpp>
#include <ql/instruments/europeanoption.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/yield/zerocurve.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/math/optimization/levenbergmarquardt.hpp>
#include <ql/pricingengines/vanilla/batesengine.hpp>
#include <ql/pricingengines/vanilla/jumpdiffusionengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/mceuropeanhestonengine.hpp>
#include <ql/pricingengines/vanilla/fdbatesvanillaengine.hpp>
#include <ql/models/equity/batesmodel.hpp>
#include <ql/models/equity/hestonmodelhelper.hpp>
#include <ql/time/period.hpp>
#include <ql/quotes/simplequote.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(BatesModelTests)
Real getCalibrationError(std::vector<ext::shared_ptr<BlackCalibrationHelper> > & options) {
Real sse = 0;
for (auto& option : options) {
const Real diff = option->calibrationError() * 100.0;
sse += diff*diff;
}
return sse;
}
struct HestonModelData {
const char* const name;
Real v0;
Real kappa;
Real theta;
Real sigma;
Real rho;
Real r;
Real q;
};
HestonModelData hestonModels[] = {
// ADI finite difference schemes for option pricing in the
// Heston model with correlation, K.J. in t'Hout and S. Foulon,
{"'t Hout case 1", 0.04, 1.5, 0.04, 0.3, -0.9, 0.025, 0.0},
// Efficient numerical methods for pricing American options under
// stochastic volatility, Samuli Ikonen and Jari Toivanen,
{"Ikonen-Toivanen", 0.0625, 5, 0.16, 0.9, 0.1, 0.1, 0.0},
// Not-so-complex logarithms in the Heston model,
// Christian Kahl and Peter Jäckel
{"Kahl-Jaeckel", 0.16, 1.0, 0.16, 2.0, -0.8, 0.0, 0.0},
// self defined test cases
{"Equity case", 0.07, 2.0, 0.04, 0.55, -0.8, 0.03, 0.035 },
};
BOOST_AUTO_TEST_CASE(testAnalyticVsBlack) {
BOOST_TEST_MESSAGE("Testing analytic Bates engine against Black formula...");
Date settlementDate = Date::todaysDate();
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = ActualActual(ActualActual::ISDA);
Date exerciseDate = settlementDate + 6*Months;
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Put, 30));
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exerciseDate));
Handle<YieldTermStructure> riskFreeTS(flatRate(0.1, dayCounter));
Handle<YieldTermStructure> dividendTS(flatRate(0.04, dayCounter));
Handle<Quote> s0(ext::shared_ptr<Quote>(new SimpleQuote(32.0)));
Real yearFraction = dayCounter.yearFraction(settlementDate, exerciseDate);
Real forwardPrice = s0->value()*std::exp((0.1-0.04)*yearFraction);
Real expected = blackFormula(payoff->optionType(), payoff->strike(),
forwardPrice, std::sqrt(0.05*yearFraction)) *
std::exp(-0.1*yearFraction);
const Real v0 = 0.05;
const Real kappa = 5.0;
const Real theta = 0.05;
const Real sigma = 1.0e-4;
const Real rho = 0.0;
const Real lambda = 0.0001;
const Real nu = 0.0;
const Real delta = 0.0001;
VanillaOption option(payoff, exercise);
ext::shared_ptr<BatesProcess> process(
new BatesProcess(riskFreeTS, dividendTS, s0, v0,
kappa, theta, sigma, rho, lambda, nu, delta));
ext::shared_ptr<PricingEngine> engine(new BatesEngine(
ext::make_shared<BatesModel>(process), 64));
option.setPricingEngine(engine);
Real calculated = option.NPV();
Real tolerance = 2.0e-7;
Real error = std::fabs(calculated - expected);
if (error > tolerance) {
BOOST_ERROR("failed to reproduce Black price with BatesEngine"
<< std::fixed
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< std::scientific
<< "\n error: " << error);
}
engine = ext::shared_ptr<PricingEngine>(new BatesDetJumpEngine(
ext::make_shared<BatesDetJumpModel>(
process, 1.0, 0.0001), 64));
option.setPricingEngine(engine);
calculated = option.NPV();
error = std::fabs(calculated - expected);
if (error > tolerance) {
BOOST_ERROR("failed to reproduce Black price with " \
"BatesDetJumpEngine"
<< std::fixed
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< std::scientific
<< "\n error: " << error);
}
engine = ext::shared_ptr<PricingEngine>(new BatesDoubleExpEngine(
ext::make_shared<BatesDoubleExpModel>(
process, 0.0001, 0.0001, 0.0001), 64));
option.setPricingEngine(engine);
calculated = option.NPV();
error = std::fabs(calculated - expected);
if (error > tolerance) {
BOOST_ERROR("failed to reproduce Black price with BatesDoubleExpEngine"
<< std::fixed
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< std::scientific
<< "\n error: " << error);
}
engine = ext::shared_ptr<PricingEngine>(new BatesDoubleExpDetJumpEngine(
ext::make_shared<BatesDoubleExpDetJumpModel>(
process, 0.0001, 0.0001, 0.0001, 0.5, 1.0, 0.0001), 64));
option.setPricingEngine(engine);
calculated = option.NPV();
error = std::fabs(calculated - expected);
if (error > tolerance) {
BOOST_ERROR("failed to reproduce Black price with " \
"BatesDoubleExpDetJumpEngine"
<< std::fixed
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< std::scientific
<< "\n error: " << error);
}
}
BOOST_AUTO_TEST_CASE(testAnalyticAndMcVsJumpDiffusion) {
BOOST_TEST_MESSAGE("Testing analytic Bates engine against Merton-76 engine...");
Date settlementDate = Date::todaysDate();
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = ActualActual(ActualActual::ISDA);
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Put, 95));
Handle<YieldTermStructure> riskFreeTS(flatRate(0.1, dayCounter));
Handle<YieldTermStructure> dividendTS(flatRate(0.04, dayCounter));
Handle<Quote> s0(ext::shared_ptr<Quote>(new SimpleQuote(100)));
Real v0 = 0.0433;
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(std::sqrt(v0)));
ext::shared_ptr<BlackVolTermStructure> volTS =
flatVol(settlementDate, vol, dayCounter);
const Real kappa = 0.5;
const Real theta = v0;
const Real sigma = 1.0e-4;
const Real rho = 0.0;
ext::shared_ptr<SimpleQuote> jumpIntensity(new SimpleQuote(2));
ext::shared_ptr<SimpleQuote> meanLogJump(new SimpleQuote(-0.2));
ext::shared_ptr<SimpleQuote> jumpVol(new SimpleQuote(0.2));
ext::shared_ptr<BatesProcess> batesProcess(new BatesProcess(
riskFreeTS, dividendTS, s0, v0, kappa, theta, sigma, rho,
jumpIntensity->value(), meanLogJump->value(), jumpVol->value()));
ext::shared_ptr<Merton76Process> mertonProcess(
new Merton76Process(s0, dividendTS, riskFreeTS,
Handle<BlackVolTermStructure>(volTS),
Handle<Quote>(jumpIntensity),
Handle<Quote>(meanLogJump),
Handle<Quote>(jumpVol)));
ext::shared_ptr<PricingEngine> batesEngine(new BatesEngine(
ext::make_shared<BatesModel>(batesProcess), 160));
const Real mcTol = 0.1;
ext::shared_ptr<PricingEngine> mcBatesEngine =
MakeMCEuropeanHestonEngine<PseudoRandom>(batesProcess)
.withStepsPerYear(2)
.withAntitheticVariate()
.withAbsoluteTolerance(mcTol)
.withSeed(1234);
ext::shared_ptr<PricingEngine> mertonEngine(
new JumpDiffusionEngine(mertonProcess, 1e-10, 1000));
for (Integer i=1; i<=5; i+=2) {
Date exerciseDate = settlementDate + i*Years;
ext::shared_ptr<Exercise> exercise(
new EuropeanExercise(exerciseDate));
VanillaOption batesOption(payoff, exercise);
batesOption.setPricingEngine(batesEngine);
Real calculated = batesOption.NPV();
batesOption.setPricingEngine(mcBatesEngine);
Real mcCalculated = batesOption.NPV();
EuropeanOption mertonOption(payoff, exercise);
mertonOption.setPricingEngine(mertonEngine);
Real expected = mertonOption.NPV();
Real tolerance = 2e-8;
Real relError = std::fabs(calculated - expected)/expected;
if (relError > tolerance) {
BOOST_FAIL("failed to reproduce Merton76 price with semi "
"analytic BatesEngine"
<< std::fixed << std::setprecision(8)
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< "\n rel. error: " << relError
<< "\n tolerance: " << tolerance);
}
Real mcError = std::fabs(expected - mcCalculated);
if (mcError > 3*mcTol) {
BOOST_FAIL("failed to reproduce Merton76 price with Monte-Carlo "
"BatesEngine"
<< std::fixed << std::setprecision(8)
<< "\n calculated: " << mcCalculated
<< "\n expected: " << expected
<< "\n error: " << mcError
<< "\n tolerance: " << mcTol);
}
}
}
BOOST_AUTO_TEST_CASE(testAnalyticVsMCPricing) {
BOOST_TEST_MESSAGE("Testing analytic Bates engine against Monte-Carlo "
"engine...");
Date settlementDate(30, March, 2007);
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = ActualActual(ActualActual::ISDA);
Date exerciseDate(30, March, 2012);
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Put, 100));
ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exerciseDate));
for (auto& hestonModel : hestonModels) {
Handle<YieldTermStructure> riskFreeTS(flatRate(hestonModel.r, dayCounter));
Handle<YieldTermStructure> dividendTS(flatRate(hestonModel.q, dayCounter));
Handle<Quote> s0(ext::shared_ptr<Quote>(new SimpleQuote(100)));
ext::shared_ptr<BatesProcess> batesProcess(new BatesProcess(
riskFreeTS, dividendTS, s0, hestonModel.v0, hestonModel.kappa, hestonModel.theta,
hestonModel.sigma, hestonModel.rho, 2.0, -0.2, 0.1));
const Real mcTolerance = 0.5;
ext::shared_ptr<PricingEngine> mcEngine =
MakeMCEuropeanHestonEngine<PseudoRandom>(batesProcess)
.withStepsPerYear(20)
.withAntitheticVariate()
.withAbsoluteTolerance(mcTolerance)
.withSeed(1234);
ext::shared_ptr<BatesModel> batesModel(new BatesModel(batesProcess));
ext::shared_ptr<PricingEngine> fdEngine(
new FdBatesVanillaEngine(batesModel, 50, 100, 30));
ext::shared_ptr<PricingEngine> analyticEngine(
new BatesEngine(batesModel, 160));
VanillaOption option(payoff, exercise);
option.setPricingEngine(mcEngine);
const Real calculated = option.NPV();
option.setPricingEngine(analyticEngine);
const Real expected = option.NPV();
option.setPricingEngine(fdEngine);
const Real fdCalculated = option.NPV();
const Real mcError = std::fabs(calculated - expected);
if (mcError > 3*mcTolerance) {
BOOST_FAIL("failed to reproduce Monte-Carlo price for BatesEngine"
<< "\n parameter: " << hestonModel.name << std::fixed
<< std::setprecision(8) << "\n calculated: " << calculated
<< "\n expected: " << expected << "\n error: " << mcError
<< "\n tolerance: " << mcTolerance);
}
const Real fdTolerance = 0.2;
const Real fdError = std::fabs(fdCalculated - expected);
if (fdError > fdTolerance) {
BOOST_FAIL("failed to reproduce PIDE price for BatesEngine"
<< "\n parameter: " << hestonModel.name << std::fixed
<< std::setprecision(8) << "\n calculated: " << fdCalculated
<< "\n expected: " << expected << "\n error: " << fdError
<< "\n tolerance: " << fdTolerance);
}
}
}
BOOST_AUTO_TEST_CASE(testDAXCalibration) {
/* this example is taken from A. Sepp
Pricing European-Style Options under Jump Diffusion Processes
with Stochstic Volatility: Applications of Fourier Transform
http://math.ut.ee/~spartak/papers/stochjumpvols.pdf
*/
BOOST_TEST_MESSAGE(
"Testing Bates model calibration using DAX volatility data...");
Date settlementDate(5, July, 2002);
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = Actual365Fixed();
Calendar calendar = TARGET();
Integer t[] = { 13, 41, 75, 165, 256, 345, 524, 703 };
Rate r[] = { 0.0357,0.0349,0.0341,0.0355,0.0359,0.0368,0.0386,0.0401 };
std::vector<Date> dates;
std::vector<Rate> rates;
dates.push_back(settlementDate);
rates.push_back(0.0357);
for (Size i = 0; i < 8; ++i) {
dates.push_back(settlementDate + t[i]);
rates.push_back(r[i]);
}
Handle<YieldTermStructure> riskFreeTS(
ext::shared_ptr<YieldTermStructure>(
new ZeroCurve(dates, rates, dayCounter)));
Handle<YieldTermStructure> dividendTS(
flatRate(settlementDate, 0.0, dayCounter));
Volatility v[] =
{ 0.6625,0.4875,0.4204,0.3667,0.3431,0.3267,0.3121,0.3121,
0.6007,0.4543,0.3967,0.3511,0.3279,0.3154,0.2984,0.2921,
0.5084,0.4221,0.3718,0.3327,0.3155,0.3027,0.2919,0.2889,
0.4541,0.3869,0.3492,0.3149,0.2963,0.2926,0.2819,0.2800,
0.4060,0.3607,0.3330,0.2999,0.2887,0.2811,0.2751,0.2775,
0.3726,0.3396,0.3108,0.2781,0.2788,0.2722,0.2661,0.2686,
0.3550,0.3277,0.3012,0.2781,0.2781,0.2661,0.2661,0.2681,
0.3428,0.3209,0.2958,0.2740,0.2688,0.2627,0.2580,0.2620,
0.3302,0.3062,0.2799,0.2631,0.2573,0.2533,0.2504,0.2544,
0.3343,0.2959,0.2705,0.2540,0.2504,0.2464,0.2448,0.2462,
0.3460,0.2845,0.2624,0.2463,0.2425,0.2385,0.2373,0.2422,
0.3857,0.2860,0.2578,0.2399,0.2357,0.2327,0.2312,0.2351,
0.3976,0.2860,0.2607,0.2356,0.2297,0.2268,0.2241,0.2320 };
Handle<Quote> s0(ext::shared_ptr<Quote>(new SimpleQuote(4468.17)));
Real strike[] = { 3400,3600,3800,4000,4200,4400,
4500,4600,4800,5000,5200,5400,5600 };
Real v0 = 0.0433;
ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(std::sqrt(v0)));
const Real kappa = 1.0;
const Real theta = v0;
const Real sigma = 1.0;
const Real rho = 0.0;
const Real lambda = 1.1098;
const Real nu = -0.1285;
const Real delta = 0.1702;
ext::shared_ptr<BatesProcess> process(
new BatesProcess(riskFreeTS, dividendTS, s0, v0,
kappa, theta, sigma, rho, lambda, nu, delta));
ext::shared_ptr<BatesModel> batesModel(new BatesModel(process));
ext::shared_ptr<PricingEngine> batesEngine(
new BatesEngine(batesModel, 64));
std::vector<ext::shared_ptr<BlackCalibrationHelper> > options;
for (Size s = 0; s < 13; ++s) {
for (Size m = 0; m < 8; ++m) {
Handle<Quote> vol(ext::shared_ptr<Quote>(
new SimpleQuote(v[s*8+m])));
Period maturity((int)((t[m]+3)/7.), Weeks); // round to weeks
// this is the calibration helper for the bates models
options.push_back(ext::shared_ptr<BlackCalibrationHelper>(
new HestonModelHelper(maturity, calendar,
s0->value(), strike[s], vol,
riskFreeTS, dividendTS,
BlackCalibrationHelper::ImpliedVolError)));
options.back()->setPricingEngine(batesEngine);
}
}
// check calibration engine
LevenbergMarquardt om;
batesModel->calibrate(std::vector<ext::shared_ptr<CalibrationHelper> >(options.begin(), options.end()),
om, EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8));
Real expected = 36.6;
Real calculated = getCalibrationError(options);
if (std::fabs(calculated - expected) > 2.5)
BOOST_ERROR("failed to calibrate the bates model"
<< "\n calculated: " << calculated
<< "\n expected: " << expected);
//check pricing of derived engines
std::vector<ext::shared_ptr<PricingEngine> > pricingEngines;
process = ext::make_shared<BatesProcess>(
riskFreeTS, dividendTS, s0, v0,
kappa, theta, sigma, rho, 1.0, -0.1, 0.1);
pricingEngines.push_back(ext::shared_ptr<PricingEngine>(
new BatesDetJumpEngine(
ext::make_shared<BatesDetJumpModel>(
process), 64)) );
ext::shared_ptr<HestonProcess> hestonProcess(new HestonProcess(
riskFreeTS, dividendTS, s0, v0, kappa, theta, sigma, rho));
pricingEngines.push_back(ext::shared_ptr<PricingEngine>(
new BatesDoubleExpEngine(
ext::make_shared<BatesDoubleExpModel>(
hestonProcess, 1.0), 64)) );
pricingEngines.push_back(ext::shared_ptr<PricingEngine>(
new BatesDoubleExpDetJumpEngine(
ext::make_shared<BatesDoubleExpDetJumpModel>(
hestonProcess, 1.0), 64)) );
Real expectedValues[] = { 5896.37,
5499.29,
6497.89};
Real tolerance=0.1;
for (Size i = 0; i < pricingEngines.size(); ++i) {
for (auto& option : options) {
option->setPricingEngine(pricingEngines[i]);
}
Real calculated = std::fabs(getCalibrationError(options));
if (std::fabs(calculated - expectedValues[i]) > tolerance)
BOOST_ERROR("failed to calculated prices for derived Bates models"
<< "\n calculated: " << calculated
<< "\n expected: " << expectedValues[i]);
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
