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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2005 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 "batesmodel.hpp"
#include "utilities.hpp"
#include <ql/time/calendars/target.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/models/equity/batesmodel.hpp>
#include <ql/models/equity/hestonmodelhelper.hpp>
#include <ql/time/period.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
QL_BEGIN_TEST_LOCALS(BatesModelTest)
Real getCalibrationError(
std::vector<boost::shared_ptr<CalibrationHelper> > & options) {
Real sse = 0;
for (Size i = 0; i < options.size(); ++i) {
const Real diff = options[i]->calibrationError()*100.0;
sse += diff*diff;
}
return sse;
}
QL_END_TEST_LOCALS(BatesModelTest)
void BatesModelTest::testAnalyticVsBlack() {
BOOST_MESSAGE("Testing analytic Bates engine against Black formula...");
SavedSettings backup;
Date settlementDate = Date::todaysDate();
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = ActualActual();
Date exerciseDate = settlementDate + 6*Months;
boost::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Put, 30));
boost::shared_ptr<Exercise> exercise(new EuropeanExercise(exerciseDate));
Handle<YieldTermStructure> riskFreeTS(flatRate(0.1, dayCounter));
Handle<YieldTermStructure> dividendTS(flatRate(0.04, dayCounter));
Handle<Quote> s0(boost::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;
VanillaOption option(payoff, exercise);
boost::shared_ptr<HestonProcess> process(new HestonProcess(
riskFreeTS, dividendTS, s0, v0, kappa, theta, sigma, rho));
boost::shared_ptr<PricingEngine> engine(new BatesEngine(
boost::shared_ptr<BatesModel>(
new BatesModel(process, 0.0001, 0, 0.0001)), 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"
<< QL_FIXED
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< QL_SCIENTIFIC
<< "\n error: " << error);
}
engine = boost::shared_ptr<PricingEngine>(new BatesDetJumpEngine(
boost::shared_ptr<BatesDetJumpModel>(
new BatesDetJumpModel(
process, 0.0001, 0.0, 0.0001, 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"
<< QL_FIXED
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< QL_SCIENTIFIC
<< "\n error: " << error);
}
engine = boost::shared_ptr<PricingEngine>(new BatesDoubleExpEngine(
boost::shared_ptr<BatesDoubleExpModel>(
new 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"
<< QL_FIXED
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< QL_SCIENTIFIC
<< "\n error: " << error);
}
engine = boost::shared_ptr<PricingEngine>(new BatesDoubleExpDetJumpEngine(
boost::shared_ptr<BatesDoubleExpDetJumpModel>(
new 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"
<< QL_FIXED
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< QL_SCIENTIFIC
<< "\n error: " << error);
}
}
void BatesModelTest::testAnalyticVsJumpDiffusion() {
BOOST_MESSAGE("Testing analytic Bates engine against Merton-76 engine...");
SavedSettings backup;
Date settlementDate = Date::todaysDate();
Settings::instance().evaluationDate() = settlementDate;
DayCounter dayCounter = ActualActual();
boost::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(boost::shared_ptr<Quote>(new SimpleQuote(100)));
Real v0 = 0.0433;
// FLOATING_POINT_EXCEPTION
boost::shared_ptr<SimpleQuote> vol(new SimpleQuote(std::sqrt(v0)));
boost::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;
boost::shared_ptr<HestonProcess> process(new HestonProcess(
riskFreeTS, dividendTS, s0, v0, kappa, theta, sigma, rho));
boost::shared_ptr<SimpleQuote> jumpIntensity(new SimpleQuote(2));
boost::shared_ptr<SimpleQuote> meanLogJump(new SimpleQuote(-0.2));
boost::shared_ptr<SimpleQuote> jumpVol(new SimpleQuote(0.2));
boost::shared_ptr<PricingEngine> batesEngine(new BatesEngine(
boost::shared_ptr<BatesModel>(
new BatesModel(process,
jumpIntensity->value(),
meanLogJump->value(),
jumpVol->value())), 160));
boost::shared_ptr<Merton76Process> stochProcess(
new Merton76Process(s0,
dividendTS,
riskFreeTS,
Handle<BlackVolTermStructure>(volTS),
Handle<Quote>(jumpIntensity),
Handle<Quote>(meanLogJump),
Handle<Quote>(jumpVol)));
boost::shared_ptr<PricingEngine> mertonEngine(
new JumpDiffusionEngine(stochProcess, 1e-10, 1000));
for (Integer i=1; i<48; ++i) {
Date exerciseDate = settlementDate + i*Months;
boost::shared_ptr<Exercise> exercise(
new EuropeanExercise(exerciseDate));
VanillaOption batesOption(payoff, exercise);
batesOption.setPricingEngine(batesEngine);
// FLOATING_POINT_EXCEPTION
Real calculated = 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 BatesEngine"
<< QL_FIXED << std::setprecision(8)
<< "\n calculated: " << calculated
<< "\n expected: " << expected
<< "\n rel. error: " << relError
<< "\n tolerance: " << tolerance);
}
}
}
void BatesModelTest::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_MESSAGE(
"Testing Bates model calibration using DAX volatility data...");
SavedSettings backup;
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]);
}
// FLOATING_POINT_EXCEPTION
Handle<YieldTermStructure> riskFreeTS(
boost::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(boost::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;
boost::shared_ptr<SimpleQuote> vol(new SimpleQuote(std::sqrt(v0)));
boost::shared_ptr<BlackVolTermStructure> volTS =
flatVol(settlementDate, vol, dayCounter);
const Real kappa = 1.0;
const Real theta = v0;
const Real sigma = 1.0;
const Real rho = 0.0;
boost::shared_ptr<HestonProcess> process(new HestonProcess(
riskFreeTS, dividendTS, s0, v0, kappa, theta, sigma, rho));
boost::shared_ptr<BatesModel> batesModel(
new BatesModel(process,1.1098, -0.1285, 0.1702));
boost::shared_ptr<PricingEngine> batesEngine(
new BatesEngine(batesModel));
std::vector<boost::shared_ptr<CalibrationHelper> > options;
for (Size s = 0; s < 13; ++s) {
for (Size m = 0; m < 8; ++m) {
Handle<Quote> vol(boost::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
// FLOATING_POINT_EXCEPTION
options.push_back(boost::shared_ptr<CalibrationHelper>(
new HestonModelHelper(maturity, calendar,
s0->value(), strike[s], vol,
riskFreeTS, dividendTS, true)));
options.back()->setPricingEngine(batesEngine);
}
}
// check calibration engine
LevenbergMarquardt om;
batesModel->calibrate(options, 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
// reset process
process = boost::shared_ptr<HestonProcess>(new HestonProcess(
riskFreeTS, dividendTS, s0, v0, kappa, theta, sigma, rho));
std::vector<boost::shared_ptr<PricingEngine> > pricingEngines;
pricingEngines.push_back(boost::shared_ptr<PricingEngine>(
new BatesDetJumpEngine(
boost::shared_ptr<BatesDetJumpModel>(
new BatesDetJumpModel(process, 1, -0.1)))) );
pricingEngines.push_back(boost::shared_ptr<PricingEngine>(
new BatesDoubleExpEngine(
boost::shared_ptr<BatesDoubleExpModel>(
new BatesDoubleExpModel(process, 1.0)))) );
pricingEngines.push_back(boost::shared_ptr<PricingEngine>(
new BatesDoubleExpDetJumpEngine(
boost::shared_ptr<BatesDoubleExpDetJumpModel>(
new BatesDoubleExpDetJumpModel(process, 1.0)))) );
Real expectedValues[] = { 5896.37,
5499.29,
6497.89};
Real tolerance=0.1;
for (Size i = 0; i < pricingEngines.size(); ++i) {
for (Size j = 0; j < options.size(); ++j) {
options[j]->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]);
}
}
test_suite* BatesModelTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("Bates model tests");
suite->add(BOOST_TEST_CASE(&BatesModelTest::testAnalyticVsBlack));
// FLOATING_POINT_EXCEPTION
suite->add(BOOST_TEST_CASE(&BatesModelTest::testAnalyticVsJumpDiffusion));
// FLOATING_POINT_EXCEPTION
suite->add(BOOST_TEST_CASE(&BatesModelTest::testDAXCalibration));
return suite;
}
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