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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2019 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
<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/termstructures/yield/fittedbonddiscountcurve.hpp>
#include <ql/termstructures/yield/nonlinearfittingmethods.hpp>
#include <ql/indexes/ibor/cdor.hpp>
#include <ql/instruments/bonds/zerocouponbond.hpp>
#include <ql/instruments/bonds/floatingratebond.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/calendars/canada.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/pricingengines/bond/discountingbondengine.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(FittedBondDiscountCurveTests)
BOOST_AUTO_TEST_CASE(testEvaluation) {
BOOST_TEST_MESSAGE("Testing that fitted bond curves work as evaluators...");
Date today = Settings::instance().evaluationDate();
Date maxDate = today + Period(10, Years);
ExponentialSplinesFitting fittingMethod;
Array parameters = {
-51293.44,
-212240.36,
168668.51,
88792.74,
120712.13,
-34332.83,
-66479.66,
13605.17,
0.0
};
FittedBondDiscountCurve curve1(
today, fittingMethod, parameters, maxDate, Actual365Fixed());
FittedBondDiscountCurve curve2(
0, TARGET(), fittingMethod, parameters, maxDate, Actual365Fixed());
// they work...
BOOST_CHECK_NO_THROW(curve1.discount(3.0));
BOOST_CHECK_NO_THROW(curve2.discount(3.0));
// ...but not after the max date
BOOST_CHECK_EXCEPTION(curve1.discount(12.0), Error,
ExpectedErrorMessage("past max curve time"));
BOOST_CHECK_EXCEPTION(curve2.discount(12.0), Error,
ExpectedErrorMessage("past max curve time"));
}
BOOST_AUTO_TEST_CASE(testFlatExtrapolation) {
BOOST_TEST_MESSAGE("Testing fitted bond curve with flat extrapolation...");
Date asof(15, Jul, 2019);
Settings::instance().evaluationDate() = asof;
// market quotes for bonds below
Real quotes[] = {101.2100, 100.6270, 99.9210, 101.6700};
std::vector<ext::shared_ptr<Bond> > bonds;
// EJ5346956
bonds.push_back(ext::make_shared<FixedRateBond>(
2, 100.0,
Schedule(Date(1, Feb, 2013), Date(3, Feb, 2020), 6 * Months, Canada(), Following, Following,
DateGeneration::Forward, false, Date(3, Aug, 2013)),
std::vector<Real>(1, 0.046), ActualActual(ActualActual::ISDA)));
// EK9689119
bonds.push_back(ext::make_shared<FixedRateBond>(
2, 100.0,
Schedule(Date(12, Jun, 2015), Date(12, Jun, 2020), 6 * Months, Canada(), Following,
Following, DateGeneration::Forward, false, Date(12, Dec, 2015)),
std::vector<Real>(1, 0.0295), ActualActual(ActualActual::ISDA)));
// AQ1410069
bonds.push_back(ext::make_shared<FixedRateBond>(
2, 100.0,
Schedule(Date(24, Nov, 2017), Date(24, Nov, 2020), 6 * Months, Canada(), Following,
Following, DateGeneration::Forward, false, Date(24, May, 2018)),
std::vector<Real>(1, 0.02689), ActualActual(ActualActual::ISDA)));
// AM5387676
bonds.push_back(ext::make_shared<FixedRateBond>(
2, 100.0,
Schedule(Date(21, Feb, 2017), Date(21, Feb, 2022), 6 * Months, Canada(), Following,
Following, DateGeneration::Forward, false, Date(21, Aug, 2017)),
std::vector<Real>(1, 0.0338), ActualActual(ActualActual::ISDA)));
std::vector<ext::shared_ptr<BondHelper> > helpers;
helpers.reserve(bonds.size());
for (Size i = 0; i < bonds.size(); ++i) {
helpers.push_back(ext::make_shared<BondHelper>(
Handle<Quote>(ext::make_shared<SimpleQuote>(quotes[i])), bonds[i]));
}
// method1 with the usual extrapolation
NelsonSiegelFitting method1;
// method2 extrapoates flat before the first and after the last bond maturity
NelsonSiegelFitting method2(
Array(), ext::shared_ptr<OptimizationMethod>(), Array(),
Actual365Fixed().yearFraction(asof, helpers.front()->bond()->maturityDate()),
Actual365Fixed().yearFraction(asof, helpers.back()->bond()->maturityDate()));
// Set a guess that will provoke a "bad" calibration for method1, actually this result was
// observed as a real calibration outcome given the default guess. The setup was more
// elaborate though and we do not aim to replicate that here.
Array guess = { 0.0317, 5.0, -3.6796, 24.1703 };
// build the fitted bond curves
ext::shared_ptr<FittedBondDiscountCurve> curve1 = ext::make_shared<FittedBondDiscountCurve>(
asof, helpers, Actual365Fixed(), method1, 1E-10, 10000, guess);
ext::shared_ptr<FittedBondDiscountCurve> curve2 = ext::make_shared<FittedBondDiscountCurve>(
asof, helpers, Actual365Fixed(), method2, 1E-10, 10000, guess);
curve1->enableExtrapolation();
curve2->enableExtrapolation();
// extract the model prices using the two curves
std::vector<Bond::Price> modelPrices1, modelPrices2;
ext::shared_ptr<PricingEngine> engine1 =
ext::make_shared<DiscountingBondEngine>(Handle<YieldTermStructure>(curve1));
ext::shared_ptr<PricingEngine> engine2 =
ext::make_shared<DiscountingBondEngine>(Handle<YieldTermStructure>(curve2));
for (auto& bond : bonds) {
bond->setPricingEngine(engine1);
modelPrices1.emplace_back(bond->cleanPrice(), Bond::Price::Clean);
bond->setPricingEngine(engine2);
modelPrices2.emplace_back(bond->cleanPrice(), Bond::Price::Clean);
}
BOOST_CHECK_EQUAL(curve1->fitResults().errorCode(), EndCriteria::MaxIterations);
BOOST_CHECK_EQUAL(curve2->fitResults().errorCode(), EndCriteria::MaxIterations);
// the resulting cost values are similar for both approaches
// i.e. the fit has a similar quality, I get for example:
// fitted curve cost1 = 0.0921232
// fitted curve cost2 = 0.0919438
// Real cost1 = std::sqrt(curve1->fitResults().minimumCostValue());
// Real cost2 = std::sqrt(curve2->fitResults().minimumCostValue());
// It turns out that the model yields are quite close for model1 and model2 while the curve
// yields are hugely different: for model1 the yields are completely off (>> 100%) while for
// model2 they are close to the bond model yields, as it should be.
//
// The reason why model1 produces reasonable bond yields is that the compounding from the
// evaluation date to the settlement date of the bonds compensates for the discounting of
// the bond flows in the "right way", although the level of the curve yields is completely
// off. I get these results:
//
// helper maturity market yield model yield 1 model yield 2 curve yield 1 curve yield 2
// 0 0.556164 0.0235711 0.0235647 0.0235709 8.69643 0.0235709
// 1 0.912329 0.0222977 0.0231515 0.0231468 5.31326 0.0231466
// 2 1.36438 0.0272363 0.0254977 0.0255014 3.56288 0.025524
// 3 2.61096 0.0268932 0.0277398 0.0277418 1.87629 0.0278147
for (Size i = 0; i < helpers.size(); ++i) {
Real t = curve1->timeFromReference(helpers[i]->bond()->maturityDate());
// Real marketYield = bonds[i]->yield(quotes[i], Actual365Fixed(), Continuous, NoFrequency);
// Real modelYield1 = bonds[i]->yield(modelPrices1[i], Actual365Fixed(), Continuous, NoFrequency);
Real modelYield2 =
bonds[i]->yield(modelPrices2[i], Actual365Fixed(), Continuous, NoFrequency);
Real curveYield1 = curve1->zeroRate(t, Continuous).rate();
Real curveYield2 = curve2->zeroRate(t, Continuous).rate();
if (curveYield1 < 1.0) {
BOOST_ERROR("Expecting huge yield; the test premise might be outdated");
}
QL_CHECK_CLOSE(modelYield2, curveYield2, 1.0); // 1.0 percent relative tolerance
}
// resetting the guess changes the calibration
curve1->resetGuess({ 0.02, 0.0, 0.0, 0.0 });
BOOST_CHECK_EQUAL(curve1->fitResults().errorCode(), EndCriteria::StationaryPoint);
for (Size i = 0; i < helpers.size(); ++i) {
Real t = curve1->timeFromReference(helpers[i]->bond()->maturityDate());
Real modelYield1 = bonds[i]->yield(modelPrices1[i], Actual365Fixed(), Continuous, NoFrequency);
Real curveYield1 = curve1->zeroRate(t, Continuous).rate();
QL_CHECK_CLOSE(modelYield1, curveYield1, 6); // somewhat better, within a dozen bps
}
}
BOOST_AUTO_TEST_CASE(testRequiredGuess) {
BOOST_TEST_MESSAGE("Testing that fitted bond curves require a guess when given an L2 penalty...");
Date today = Settings::instance().evaluationDate();
auto bond1 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(1, Years));
auto bond2 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(2, Years));
auto bond3 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(5, Years));
auto bond4 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(10, Years));
std::vector<ext::shared_ptr<BondHelper> > helpers(4);
helpers[0] = ext::make_shared<BondHelper>(makeQuoteHandle(99.0), bond1);
helpers[1] = ext::make_shared<BondHelper>(makeQuoteHandle(98.0), bond2);
helpers[2] = ext::make_shared<BondHelper>(makeQuoteHandle(95.0), bond3);
helpers[3] = ext::make_shared<BondHelper>(makeQuoteHandle(90.0), bond4);
Array weights = {};
ext::shared_ptr<OptimizationMethod> optimizer = {};
Array l2 = { 0.25, 0.25, 0.25, 0.25 };
NelsonSiegelFitting fittingMethod(weights, optimizer, l2);
Real accuracy = 1e-10;
Size maxIterations = 10000;
FittedBondDiscountCurve curve(0, TARGET(), helpers, Actual365Fixed(),
fittingMethod, accuracy, maxIterations);
BOOST_CHECK_EXCEPTION(curve.discount(3.0), Error,
ExpectedErrorMessage("L2 penalty requires a guess"));
}
BOOST_AUTO_TEST_CASE(testGuessSize) {
BOOST_TEST_MESSAGE("Testing that fitted bond curves check the guess size when given...");
Date today = Settings::instance().evaluationDate();
auto bond1 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(1, Years));
auto bond2 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(2, Years));
auto bond3 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(5, Years));
auto bond4 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(10, Years));
std::vector<ext::shared_ptr<BondHelper> > helpers(4);
helpers[0] = ext::make_shared<BondHelper>(makeQuoteHandle(99.0), bond1);
helpers[1] = ext::make_shared<BondHelper>(makeQuoteHandle(98.0), bond2);
helpers[2] = ext::make_shared<BondHelper>(makeQuoteHandle(95.0), bond3);
helpers[3] = ext::make_shared<BondHelper>(makeQuoteHandle(90.0), bond4);
NelsonSiegelFitting fittingMethod;
Real accuracy = 1e-10;
Size maxIterations = 10000;
Array guess = { 0.01, 0.0, 0.0 }; // too few
FittedBondDiscountCurve curve(0, TARGET(), helpers, Actual365Fixed(),
fittingMethod, accuracy, maxIterations, guess);
BOOST_CHECK_EXCEPTION(curve.discount(3.0), Error,
ExpectedErrorMessage("wrong size for guess"));
}
BOOST_AUTO_TEST_CASE(testConstraint) {
BOOST_TEST_MESSAGE("Testing that fitted bond curves respect passed constraint...");
class FlatZero : public FittedBondDiscountCurve::FittingMethod {
public:
FlatZero(Constraint constraint = NoConstraint())
: FittedBondDiscountCurve::FittingMethod(true, // constrainAtZero
Array(), // weights
ext::shared_ptr<OptimizationMethod>(),
Array(), // l2
0.0, // minCutoffTime
QL_MAX_REAL, //maxCutoffTime
std::move(constraint)) {}
std::unique_ptr<FittedBondDiscountCurve::FittingMethod> clone() const override {
return std::make_unique<FlatZero>(*this);
}
private:
Size size() const override { return 1; }
DiscountFactor discountFunction(const Array& x, Time t) const override {
Real zeroRate = x[0];
DiscountFactor d = std::exp(-zeroRate * t);
return d;
}
};
Date today = Settings::instance().evaluationDate();
auto bond1 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(1, Years));
auto bond2 = ext::make_shared<ZeroCouponBond>(3, TARGET(), 100.0, today + Period(2, Years));
std::vector<ext::shared_ptr<BondHelper>> helpers(2);
helpers[0] = ext::make_shared<BondHelper>(makeQuoteHandle(101.0), bond1);
helpers[1] = ext::make_shared<BondHelper>(makeQuoteHandle(102.0), bond2);
Real accuracy = 1e-10; // default value
Size maxIterations = 10000; // default value
Array guess = {0.01}; // something positive so that initial value is in feasible region
FlatZero unconstrainedMethod;
FittedBondDiscountCurve unconstrainedCurve(0, TARGET(), helpers, Actual365Fixed(), unconstrainedMethod,
accuracy, maxIterations, guess);
BOOST_CHECK_LT(unconstrainedCurve.fitResults().solution()[0], 0.0);
FlatZero positiveMethod{PositiveConstraint()};
FittedBondDiscountCurve positiveCurve(0, TARGET(), helpers, Actual365Fixed(), positiveMethod,
accuracy, maxIterations, guess);
BOOST_CHECK_GT(positiveCurve.fitResults().solution()[0], 0.0);
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
