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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2020 Marcin Rybacki
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/currencies/europe.hpp>
#include <ql/indexes/iborindex.hpp>
#include <ql/math/interpolations/loginterpolation.hpp>
#include <ql/termstructures/yield/piecewiseyieldcurve.hpp>
#include <ql/termstructures/yield/ratehelpers.hpp>
#include <ql/termstructures/yield/ultimateforwardtermstructure.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/simpledaycounter.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(UltimateForwardTermStructureTests)
struct Datum {
Integer n;
TimeUnit units;
Rate rate;
};
struct LLFRWeight {
Time ttm;
Real weight;
};
struct CommonVars {
Date today, settlement;
Calendar calendar;
Natural settlementDays;
Currency ccy;
BusinessDayConvention businessConvention;
DayCounter dayCount;
Frequency fixedFrequency;
Period floatingTenor;
ext::shared_ptr<IborIndex> index;
RelinkableHandle<YieldTermStructure> ftkCurveHandle;
ext::shared_ptr<Quote> ufrRate;
Period fsp;
Real alpha;
// utilities
CommonVars() {
settlementDays = 2;
businessConvention = Unadjusted;
dayCount = SimpleDayCounter();
calendar = NullCalendar();
ccy = EURCurrency();
fixedFrequency = Annual;
floatingTenor = 6 * Months;
index = ext::make_shared<IborIndex>(
"FTK_IDX", floatingTenor, settlementDays, ccy, calendar,
businessConvention, false, dayCount, ftkCurveHandle);
/* Data source: https://fred.stlouisfed.org/
Note that these rates are used as a proxy.
In order to fully replicate the rates published by the Dutch Central Bank
(with the required accuracy) one needs to use Bloomberg CMPL BID Euribor 6m swap
rates as stated in the documentation: https://www.toezicht.dnb.nl */
Datum swapData[] = {{1, Years, -0.00315}, {2, Years, -0.00205}, {3, Years, -0.00144},
{4, Years, -0.00068}, {5, Years, 0.00014}, {6, Years, 0.00103},
{7, Years, 0.00194}, {8, Years, 0.00288}, {9, Years, 0.00381},
{10, Years, 0.00471}, {12, Years, 0.0063}, {15, Years, 0.00808},
{20, Years, 0.00973}, {25, Years, 0.01035}, {30, Years, 0.01055},
{40, Years, 0.0103}, {50, Years, 0.0103}};
InterestRate ufr(0.023, dayCount, Compounded, Annual);
ufrRate = ext::shared_ptr<Quote>(
new SimpleQuote(ufr.equivalentRate(Continuous, Annual, 1.0)));
fsp = 20 * Years;
alpha = 0.1;
today = calendar.adjust(Date(29, March, 2019));
Settings::instance().evaluationDate() = today;
settlement = calendar.advance(today, settlementDays, Days);
Size nInstruments = std::size(swapData);
std::vector<ext::shared_ptr<RateHelper> > instruments(nInstruments);
for (Size i = 0; i < nInstruments; i++) {
instruments[i] = ext::shared_ptr<RateHelper>(new SwapRateHelper(
swapData[i].rate, Period(swapData[i].n, swapData[i].units), calendar,
fixedFrequency, businessConvention, dayCount, index));
}
ext::shared_ptr<YieldTermStructure> ftkCurve(
new PiecewiseYieldCurve<Discount, LogLinear>(settlement, instruments, dayCount));
ftkCurve->enableExtrapolation();
ftkCurveHandle.linkTo(ftkCurve);
}
};
ext::shared_ptr<Quote> calculateLLFR(const Handle<YieldTermStructure>& ts, const Period& fsp) {
DayCounter dc = ts->dayCounter();
Real omega = 8.0 / 15.0;
Time cutOff = ts->timeFromReference(ts->referenceDate() + fsp);
LLFRWeight llfrWeights[] = {{25.0, 1.0}, {30.0, 0.5}, {40.0, 0.25}, {50.0, 0.125}};
Size nWeights = std::size(llfrWeights);
Rate llfr = 0.0;
for (Size j = 0; j < nWeights; j++) {
LLFRWeight w = llfrWeights[j];
llfr += w.weight * ts->forwardRate(cutOff, w.ttm, Continuous, NoFrequency, true);
}
return ext::shared_ptr<Quote>(new SimpleQuote(omega * llfr));
}
Rate calculateExtrapolatedForward(Time t, Time fsp, Rate llfr, Rate ufr, Real alpha) {
Time deltaT = t - fsp;
Real beta = (1.0 - std::exp(-alpha * deltaT)) / (alpha * deltaT);
return ufr + (llfr - ufr) * beta;
}
BOOST_AUTO_TEST_CASE(testDutchCentralBankRates) {
BOOST_TEST_MESSAGE("Testing DNB replication of UFR zero annually compounded rates...");
CommonVars vars;
ext::shared_ptr<Quote> llfr = calculateLLFR(vars.ftkCurveHandle, vars.fsp);
ext::shared_ptr<YieldTermStructure> ufrTs(
new UltimateForwardTermStructure(vars.ftkCurveHandle, Handle<Quote>(llfr),
Handle<Quote>(vars.ufrRate), vars.fsp, vars.alpha));
// Official annually compounded zero rates published
// by the Dutch Central Bank: https://statistiek.dnb.nl/
Datum expectedZeroes[] = {{10, Years, 0.00477}, {20, Years, 0.01004}, {30, Years, 0.01223},
{40, Years, 0.01433}, {50, Years, 0.01589}, {60, Years, 0.01702},
{70, Years, 0.01785}, {80, Years, 0.01849}, {90, Years, 0.01899},
{100, Years, 0.01939}};
Real tolerance = 1.0e-4;
Size nRates = std::size(expectedZeroes);
for (Size i = 0; i < nRates; ++i) {
Period p = expectedZeroes[i].n * expectedZeroes[i].units;
Date maturity = vars.settlement + p;
Rate actual = ufrTs->zeroRate(maturity, vars.dayCount, Compounded, Annual).rate();
Rate expected = expectedZeroes[i].rate;
if (std::fabs(actual - expected) > tolerance)
BOOST_ERROR("unable to reproduce zero yield rate from the UFR curve\n"
<< std::setprecision(5)
<< " calculated: " << actual << "\n"
<< " expected: " << expected << "\n"
<< " tenor: " << p << "\n");
}
}
BOOST_AUTO_TEST_CASE(testExtrapolatedForward) {
BOOST_TEST_MESSAGE("Testing continuous forward rates in extrapolation region...");
CommonVars vars;
ext::shared_ptr<Quote> llfr(new SimpleQuote(0.0125));
ext::shared_ptr<YieldTermStructure> ufrTs(
new UltimateForwardTermStructure(vars.ftkCurveHandle, Handle<Quote>(llfr),
Handle<Quote>(vars.ufrRate), vars.fsp, vars.alpha));
Time cutOff = ufrTs->timeFromReference(ufrTs->referenceDate() + vars.fsp);
Period tenors[] = {
20 * Years, 30 * Years, 40 * Years, 50 * Years, 60 * Years,
70 * Years, 80 * Years, 90 * Years, 100 * Years,
};
Size nTenors = std::size(tenors);
for (Size i = 0; i < nTenors; ++i) {
Date maturity = vars.settlement + tenors[i];
Time t = ufrTs->timeFromReference(maturity);
Rate actual = ufrTs->forwardRate(cutOff, t, Continuous, NoFrequency, true).rate();
Rate expected = calculateExtrapolatedForward(t, cutOff, llfr->value(),
vars.ufrRate->value(), vars.alpha);
Real tolerance = 1.0e-10;
if (std::fabs(actual - expected) > tolerance)
BOOST_ERROR("unable to replicate the forward rate from the UFR curve\n"
<< std::setprecision(5)
<< " calculated: " << actual << "\n"
<< " expected: " << expected << "\n"
<< " tenor: " << tenors[i] << "\n");
}
}
BOOST_AUTO_TEST_CASE(testZeroRateAtFirstSmoothingPoint) {
BOOST_TEST_MESSAGE("Testing zero rate on the first smoothing point...");
CommonVars vars;
ext::shared_ptr<Quote> llfr(new SimpleQuote(0.0125));
ext::shared_ptr<YieldTermStructure> ufrTs(
new UltimateForwardTermStructure(vars.ftkCurveHandle, Handle<Quote>(llfr),
Handle<Quote>(vars.ufrRate), vars.fsp, vars.alpha));
Time cutOff = ufrTs->timeFromReference(ufrTs->referenceDate() + vars.fsp);
Rate actual = ufrTs->zeroRate(cutOff, Continuous, NoFrequency, true).rate();
Rate expected = vars.ftkCurveHandle->zeroRate(cutOff, Continuous, NoFrequency, true).rate();
Real tolerance = 1.0e-10;
if (std::fabs(actual - expected) > tolerance)
BOOST_ERROR("unable to replicate the zero rate on the First Smoothing Point\n"
<< std::setprecision(5)
<< " calculated: " << actual << "\n"
<< " expected: " << expected << "\n"
<< " FSP: " << vars.fsp << "\n");
}
BOOST_AUTO_TEST_CASE(testThatInspectorsEqualToBaseCurve) {
BOOST_TEST_MESSAGE("Testing UFR curve inspectors...");
CommonVars vars;
ext::shared_ptr<Quote> llfr(new SimpleQuote(0.0125));
ext::shared_ptr<YieldTermStructure> ufrTs(
new UltimateForwardTermStructure(vars.ftkCurveHandle, Handle<Quote>(llfr),
Handle<Quote>(vars.ufrRate), vars.fsp, vars.alpha));
if (ufrTs->dayCounter() != vars.ftkCurveHandle->dayCounter())
BOOST_ERROR("different day counter on the UFR curve than on the base curve\n"
<< " UFR curve: " << ufrTs->dayCounter() << "\n"
<< " base curve: " << vars.ftkCurveHandle->dayCounter() << "\n");
if (ufrTs->referenceDate() != vars.ftkCurveHandle->referenceDate())
BOOST_ERROR("different reference date on the UFR curve than on the base curve\n"
<< " UFR curve: " << ufrTs->referenceDate() << "\n"
<< " base curve: " << vars.ftkCurveHandle->referenceDate() << "\n");
if (ufrTs->maxDate() == vars.ftkCurveHandle->maxDate())
BOOST_ERROR("same max date on the UFR curve as on the base curve\n"
<< " UFR curve: " << ufrTs->maxDate() << "\n"
<< " base curve: " << vars.ftkCurveHandle->maxDate() << "\n");
if (ufrTs->maxTime() == vars.ftkCurveHandle->maxTime())
BOOST_ERROR("same max time on the UFR curve as on the base curve\n"
<< " UFR curve: " << ufrTs->maxTime() << "\n"
<< " base curve: " << vars.ftkCurveHandle->maxTime() << "\n");
}
BOOST_AUTO_TEST_CASE(testExceptionWhenFspLessOrEqualZero) {
BOOST_TEST_MESSAGE("Testing exception when the first smoothing point is less than or equal to zero...");
CommonVars vars;
ext::shared_ptr<Quote> llfr(new SimpleQuote(0.0125));
BOOST_CHECK_THROW(
ext::shared_ptr<YieldTermStructure> ufrTsZeroPeriod(
new UltimateForwardTermStructure(vars.ftkCurveHandle, Handle<Quote>(llfr),
Handle<Quote>(vars.ufrRate), 0 * Years, vars.alpha)),
Error);
BOOST_CHECK_THROW(
ext::shared_ptr<YieldTermStructure> ufrTsNegativePeriod(
new UltimateForwardTermStructure(vars.ftkCurveHandle, Handle<Quote>(llfr),
Handle<Quote>(vars.ufrRate), -1 * Years, vars.alpha)),
Error);
}
BOOST_AUTO_TEST_CASE(testObservability) {
BOOST_TEST_MESSAGE("Testing observability of the UFR curve...");
CommonVars vars;
ext::shared_ptr<SimpleQuote> llfr(new SimpleQuote(0.0125));
Handle<Quote> llfr_quote(llfr);
ext::shared_ptr<SimpleQuote> ufr(new SimpleQuote(0.02));
Handle<Quote> ufr_handle(ufr);
ext::shared_ptr<YieldTermStructure> ufrTs(new UltimateForwardTermStructure(
vars.ftkCurveHandle, llfr_quote, ufr_handle, vars.fsp, vars.alpha));
Flag flag;
flag.registerWith(ufrTs);
llfr->setValue(0.012);
if (!flag.isUp())
BOOST_ERROR("Observer was not notified of LLFR change.");
flag.lower();
ufr->setValue(0.019);
if (!flag.isUp())
BOOST_ERROR("Observer was not notified of UFR change.");
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
