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gjrgarchmodel.cpp
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gjrgarchmodel.cpp
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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Yee Man Chan
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 "gjrgarchmodel.hpp"
#include "utilities.hpp"
#include <ql/processes/gjrgarchprocess.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/models/equity/gjrgarchmodel.hpp>
#include <ql/models/equity/hestonmodelhelper.hpp>
#include <ql/pricingengines/vanilla/analyticgjrgarchengine.hpp>
#include <ql/pricingengines/vanilla/mceuropeangjrgarchengine.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/actual365fixed.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/termstructures/yield/zerocurve.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/math/optimization/simplex.hpp>
#include <ql/time/period.hpp>
#include <ql/quotes/simplequote.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
void GJRGARCHModelTest::testEngines() {
BOOST_TEST_MESSAGE(
"Testing Monte Carlo GJR-GARCH engine against "
"analytic GJR-GARCH engine...");
DayCounter dayCounter = ActualActual(ActualActual::ISDA);
const Date today = Date::todaysDate();
Handle<YieldTermStructure> riskFreeTS(flatRate(today, 0.05, dayCounter));
Handle<YieldTermStructure> dividendTS(flatRate(today, 0.0, dayCounter));
const Real s0 = 50.0;
const Real omega = 2.0e-6;
const Real alpha = 0.024;
const Real beta = 0.93;
const Real gamma = 0.059;
const Real daysPerYear = 365.0; // number of trading days per year
const Size maturity[] = {90, 180};
const Real strike[] = {35,40,45,50,55,60};
const Real Lambda[] = {0.0,0.1,0.2};
Real analytic[3][2][6]; // correct values of analytic approximation
analytic[0][0][0] = 15.4315;
analytic[0][0][1] = 10.5552;
analytic[0][0][2] = 5.9625;
analytic[0][0][3] = 2.3282;
analytic[0][0][4] = 0.5408;
analytic[0][0][5] = 0.0835;
analytic[0][1][0] = 15.8969;
analytic[0][1][1] = 11.2173;
analytic[0][1][2] = 6.9112;
analytic[0][1][3] = 3.4788;
analytic[0][1][4] = 1.3769;
analytic[0][1][5] = 0.4357;
analytic[1][0][0] = 15.4556;
analytic[1][0][1] = 10.6929;
analytic[1][0][2] = 6.2381;
analytic[1][0][3] = 2.6831;
analytic[1][0][4] = 0.7822;
analytic[1][0][5] = 0.1738;
analytic[1][1][0] = 16.0587;
analytic[1][1][1] = 11.5338;
analytic[1][1][2] = 7.3170;
analytic[1][1][3] = 3.9074;
analytic[1][1][4] = 1.7279;
analytic[1][1][5] = 0.6568;
analytic[2][0][0] = 15.8000;
analytic[2][0][1] = 11.2734;
analytic[2][0][2] = 7.0376;
analytic[2][0][3] = 3.6767;
analytic[2][0][4] = 1.5871;
analytic[2][0][5] = 0.5934;
analytic[2][1][0] = 16.9286;
analytic[2][1][1] = 12.3170;
analytic[2][1][2] = 8.0405;
analytic[2][1][3] = 4.6348;
analytic[2][1][4] = 2.3429;
analytic[2][1][5] = 1.0590;
Real mcValues[3][2][6]; // correct values of Monte Carlo
mcValues[0][0][0] = 15.4332;
mcValues[0][0][1] = 10.5453;
mcValues[0][0][2] = 5.9351;
mcValues[0][0][3] = 2.3521;
mcValues[0][0][4] = 0.5597;
mcValues[0][0][5] = 0.0776;
mcValues[0][1][0] = 15.8910;
mcValues[0][1][1] = 11.1772;
mcValues[0][1][2] = 6.8827;
mcValues[0][1][3] = 3.5096;
mcValues[0][1][4] = 1.4196;
mcValues[0][1][5] = 0.4502;
mcValues[1][0][0] = 15.4580;
mcValues[1][0][1] = 10.6433;
mcValues[1][0][2] = 6.2019;
mcValues[1][0][3] = 2.7513;
mcValues[1][0][4] = 0.8374;
mcValues[1][0][5] = 0.1706;
mcValues[1][1][0] = 15.9884;
mcValues[1][1][1] = 11.4139;
mcValues[1][1][2] = 7.3103;
mcValues[1][1][3] = 4.0497;
mcValues[1][1][4] = 1.8862;
mcValues[1][1][5] = 0.7322;
mcValues[2][0][0] = 15.6619;
mcValues[2][0][1] = 11.1263;
mcValues[2][0][2] = 7.0968;
mcValues[2][0][3] = 3.9152;
mcValues[2][0][4] = 1.8133;
mcValues[2][0][5] = 0.7010;
mcValues[2][1][0] = 16.5195;
mcValues[2][1][1] = 12.3181;
mcValues[2][1][2] = 8.6085;
mcValues[2][1][3] = 5.5700;
mcValues[2][1][4] = 3.3103;
mcValues[2][1][5] = 1.8053;
for (Size k = 0; k < 3; ++k) {
Real lambda = Lambda[k];
Real m1 = beta+(alpha+gamma*CumulativeNormalDistribution()(lambda))
*(1.0+lambda*lambda)+gamma*lambda*std::exp(-lambda*lambda/2.0)
/std::sqrt(2.0*M_PI);
Real v0 = omega/(1.0-m1);
Handle<Quote> q(ext::shared_ptr<Quote>(new SimpleQuote(s0)));
ext::shared_ptr<GJRGARCHProcess> process(new GJRGARCHProcess(
riskFreeTS, dividendTS, q, v0, omega, alpha, beta, gamma, lambda, daysPerYear));
ext::shared_ptr<PricingEngine> engine1 =
MakeMCEuropeanGJRGARCHEngine<PseudoRandom>(process)
.withStepsPerYear(20)
.withAbsoluteTolerance(0.02)
.withSeed(1234);
ext::shared_ptr<PricingEngine> engine2(
new AnalyticGJRGARCHEngine(ext::make_shared<GJRGARCHModel>(
process)));
for (Size i = 0; i < 2; ++i) {
for (Size j = 0; j < 6; ++j) {
Real x = strike[j];
ext::shared_ptr<StrikedTypePayoff> payoff(
new PlainVanillaPayoff(Option::Call, x));
Date exDate = today + maturity[i];
ext::shared_ptr<Exercise> exercise(
new EuropeanExercise(exDate));
VanillaOption option(payoff, exercise);
option.setPricingEngine(engine1);
Real calculated = option.NPV();
option.setPricingEngine(engine2);
Real expected = option.NPV();
Real tolerance = 7.5e-2;
if (std::fabs(expected - analytic[k][i][j]) > 2.0*tolerance) {
BOOST_ERROR("failed to match results from engines"
<< "\n correct value: "
<< analytic[k][i][j]
<< "\n Analytic Approx.: "
<< expected
<< " +/- " << tolerance);
}
if (std::fabs(calculated-mcValues[k][i][j]) > 2.0*tolerance) {
BOOST_ERROR("failed to match results from engines"
<< "\n correct value: "
<< mcValues[k][i][j]
<< "\n Monte Carlo: " << calculated
<< " +/- " << tolerance);
}
}
}
}
}
void GJRGARCHModelTest::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 GJR-GARCH 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);
Size i;
for (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 };
std::vector<ext::shared_ptr<CalibrationHelper> > options;
const Real omega = 2.0e-6;
const Real alpha = 0.024;
const Real beta = 0.93;
const Real gamma = 0.059;
const Real lambda = 0.1;
const Real daysPerYear = 365.0; // number of trading days per year
const Real m1 = beta+(alpha+gamma*CumulativeNormalDistribution()(lambda))
*(1.0+lambda*lambda)+gamma*lambda*std::exp(-lambda*lambda/2.0)
/std::sqrt(2.0*M_PI);
const Real v0 = omega/(1.0-m1);
ext::shared_ptr<GJRGARCHProcess> process(new GJRGARCHProcess(
riskFreeTS, dividendTS, s0, v0,
omega, alpha, beta, gamma, lambda, daysPerYear));
ext::shared_ptr<GJRGARCHModel> model(new GJRGARCHModel(process));
ext::shared_ptr<PricingEngine> engine(
new AnalyticGJRGARCHEngine(ext::shared_ptr<GJRGARCHModel>(model)));
for (Size s = 3; s < 10; ++s) {
for (Size m = 0; m < 3; ++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
ext::shared_ptr<BlackCalibrationHelper> option(
new HestonModelHelper(maturity, calendar,
s0->value(), strike[s], vol,
riskFreeTS, dividendTS,
BlackCalibrationHelper::ImpliedVolError));
option->setPricingEngine(engine);
options.push_back(option);
}
}
Simplex om(0.05);
model->calibrate(options, om,
EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8));
Real sse = 0;
for (i = 0; i < options.size(); ++i) {
const Real diff = options[i]->calibrationError()*100.0;
sse += diff*diff;
}
Real maxExpected = 15;
if (sse > maxExpected) {
BOOST_FAIL("Failed to reproduce calibration error"
<< "\n calculated: " << sse
<< "\n expected: < " << maxExpected);
}
}
test_suite* GJRGARCHModelTest::suite(SpeedLevel speed) {
auto* suite = BOOST_TEST_SUITE("GJR-GARCH model tests");
if (speed <= Fast) {
suite->add(QUANTLIB_TEST_CASE(&GJRGARCHModelTest::testDAXCalibration));
}
if (speed == Slow) {
suite->add(QUANTLIB_TEST_CASE(&GJRGARCHModelTest::testEngines));
}
return suite;
}