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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012 Liquidnet Holdings, Inc.
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 "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/models/volatility/garch.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/math/optimization/levenbergmarquardt.hpp>
#include <ql/math/randomnumbers/inversecumulativerng.hpp>
#include <ql/math/randomnumbers/mt19937uniformrng.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(GARCHTests)
class DummyOptimizationMethod : public OptimizationMethod {
public:
EndCriteria::Type minimize(Problem& P, const EndCriteria& endCriteria) override {
P.setFunctionValue(P.value(P.currentValue()));
return EndCriteria::None;
}
};
struct Results {
Real alpha;
Real beta;
Real omega;
Real logLikelihood;
};
typedef InverseCumulativeRng<MersenneTwisterUniformRng,
InverseCumulativeNormal>
GaussianGenerator;
static Real expected_calc[] = {
0.452769, 0.513323, 0.530141, 0.5350841, 0.536558,
0.536999, 0.537132, 0.537171, 0.537183, 0.537187
};
void check_ts(const std::pair<Date, Volatility> &x) {
if (x.first.serialNumber() < 22835 || x.first.serialNumber() > 22844) {
BOOST_ERROR("Failed to reproduce calculated GARCH time: "
<< "\n calculated: " << x.first.serialNumber()
<< "\n expected: [22835, 22844]");
}
Real error =
std::fabs(x.second - expected_calc[x.first.serialNumber()-22835]);
if (error > 1.0e-6) {
BOOST_ERROR("Failed to reproduce calculated GARCH value at "
<< x.first.serialNumber() << ": "
<< "\n calculated: " << x.second
<< "\n expected: "
<< expected_calc[x.first.serialNumber()-22835]);
}
}
#define CHECK(results, garch, member) \
if (std::fabs(results.member - garch.member()) > 1.0e-6) { \
BOOST_ERROR("Failed to reproduce expected " #member \
<< "\n calculated: " << garch.member() \
<< "\n expected: " << results.member); \
}
BOOST_AUTO_TEST_CASE(testCalibration) {
BOOST_TEST_MESSAGE("Testing GARCH model calibration...");
Date start(7, July, 1962), d = start;
TimeSeries<Volatility> ts;
Garch11 garch(0.2, 0.3, 0.4);
GaussianGenerator rng(MersenneTwisterUniformRng(48));
Volatility r = 0.0, v = 0.0;
for (std::size_t i = 0; i < 50000; ++i, d += 1) {
v = garch.forecast(r, v);
r = rng.next().value * std::sqrt(v);
ts[d] = r;
}
// Default calibration; works fine in most cases
Garch11 cgarch1(ts);
Results calibrated = { 0.207592, 0.281979, 0.204647, -0.0217413 };
CHECK(calibrated, cgarch1, alpha);
CHECK(calibrated, cgarch1, beta);
CHECK(calibrated, cgarch1, omega);
CHECK(calibrated, cgarch1, logLikelihood);
// Type 1 initial guess - no further optimization
Garch11 cgarch2(ts, Garch11::MomentMatchingGuess);
DummyOptimizationMethod m;
cgarch2.calibrate(ts, m, EndCriteria (3, 2, 0.0, 0.0, 0.0));
Results expected1 = { 0.265749, 0.156956, 0.230964, -0.0227179 };
CHECK(expected1, cgarch2, alpha);
CHECK(expected1, cgarch2, beta);
CHECK(expected1, cgarch2, omega);
CHECK(expected1, cgarch2, logLikelihood);
// Optimization from this initial guess
cgarch2.calibrate(ts);
CHECK(calibrated, cgarch2, alpha);
CHECK(calibrated, cgarch2, beta);
CHECK(calibrated, cgarch2, omega);
CHECK(calibrated, cgarch2, logLikelihood);
// Type 2 initial guess - no further optimization
Garch11 cgarch3(ts, Garch11::GammaGuess);
cgarch3.calibrate(ts, m, EndCriteria (3, 2, 0.0, 0.0, 0.0));
Results expected2 = { 0.269896, 0.211373, 0.207534, -0.022798 };
CHECK(expected2, cgarch3, alpha);
CHECK(expected2, cgarch3, beta);
CHECK(expected2, cgarch3, omega);
CHECK(expected2, cgarch3, logLikelihood);
// Optimization from this initial guess
cgarch3.calibrate(ts);
CHECK(calibrated, cgarch3, alpha);
CHECK(calibrated, cgarch3, beta);
CHECK(calibrated, cgarch3, omega);
CHECK(calibrated, cgarch3, logLikelihood);
// Double optimization using type 1 and 2 initial guesses
Garch11 cgarch4(ts, Garch11::DoubleOptimization);
cgarch4.calibrate(ts);
CHECK(calibrated, cgarch4, alpha);
CHECK(calibrated, cgarch4, beta);
CHECK(calibrated, cgarch4, omega);
CHECK(calibrated, cgarch4, logLikelihood);
// Alternative, gradient based optimization - usually gives worse
// results than simplex
LevenbergMarquardt lm;
cgarch4.calibrate(ts, lm, EndCriteria (100000, 500, 1e-8, 1e-8, 1e-8));
Results expected3 = { 0.265196, 0.277364, 0.678812, -0.216313 };
CHECK(expected3, cgarch4, alpha);
CHECK(expected3, cgarch4, beta);
CHECK(expected3, cgarch4, omega);
CHECK(expected3, cgarch4, logLikelihood);
}
BOOST_AUTO_TEST_CASE(testCalculation) {
BOOST_TEST_MESSAGE("Testing GARCH model calculation...");
Date d(7, July, 1962);
TimeSeries<Volatility> ts;
Garch11 garch(0.2, 0.3, 0.4);
Volatility r = 0.1;
for (std::size_t i = 0; i < 10; ++i, d += 1) {
ts[d] = r;
}
TimeSeries<Volatility> tsout = garch.calculate(ts);
std::for_each(tsout.cbegin(), tsout.cend(), check_ts);
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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