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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2025 Hiroto Ogawa
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/instruments/perpetualfutures.hpp>
#include <ql/pricingengines/futures/discountingperpetualfuturesengine.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/quotes/simplequote.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(PerpetualFuturesTests)
#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoffType, fundingType, fundingFreq, s, r, q, k, iDiff, today, \
expected, calculated, relError, tolerance) \
BOOST_FAIL(payoffType \
<< " perpetual futures with " << fundingType << " funding type:\n" \
<< " spot value: " << s << "\n" \
<< " risk-free rate: " << r << "\n" \
<< " asset yield: " << q << "\n" \
<< " funding rate: " << k << "\n" \
<< " interest rate differential: " << iDiff << "\n" \
<< " funding frequency: " << fundingFreq << "\n" \
<< " reference date: " << today << "\n" \
<< " expected " << greekName << ": " << expected << "\n" \
<< " calculated " << greekName << ": " << calculated << "\n" \
<< " rel error: " << relError << "\n" \
<< " tolerance: " << tolerance << "\n");
struct PerpetualFuturesData {
PerpetualFutures::PayoffType payoffType;
PerpetualFutures::FundingType fundingType;
Period fundingFreq;
Real s; // spot
Rate r; // risk-free rate
Rate q; // asset yield
Rate k; // funding rate
Rate iDiff; // interest rate differential
Real relTol; // relative tolerance
};
BOOST_AUTO_TEST_CASE(testPerpetualFuturesValues) {
BOOST_TEST_MESSAGE("Testing perpetual futures value against analytic form for constant parameters...");
PerpetualFuturesData values[] = {
// Discrete time
{PerpetualFutures::Linear, PerpetualFutures::FundingWithPreviousSpot, Period(3, Months), 10000., 0.04, 0.02, 0.01, 0.005, 1.e-6},
{PerpetualFutures::Linear, PerpetualFutures::FundingWithCurrentSpot, Period(3, Months), 10000., 0.04, 0.02, 0.01, 0.005, 1.e-6},
{PerpetualFutures::Inverse, PerpetualFutures::FundingWithPreviousSpot, Period(3, Months), 10000., 0.04, 0.02, 0.01, 0.005, 1.e-6},
{PerpetualFutures::Inverse, PerpetualFutures::FundingWithCurrentSpot, Period(3, Months), 10000., 0.04, 0.02, 0.01, 0.005, 1.e-6},
{PerpetualFutures::Linear, PerpetualFutures::FundingWithPreviousSpot, Period(3, Months), 10000., 0.04, 0.02, 0.01, 0.005, 1.e-6},
// Continuous time
{PerpetualFutures::Linear, PerpetualFutures::FundingWithPreviousSpot, Period(0, Months), 10000., 0.04, 0.02, 0.2, 0.005, 1.e-6},
{PerpetualFutures::Inverse, PerpetualFutures::FundingWithPreviousSpot, Period(0, Months), 10000., 0.04, 0.02, 0.2, 0.005, 1.e-6},
};
DayCounter dc = ActualActual(ActualActual::ISDA);
Calendar cal = NullCalendar();
Date today = Date::todaysDate();
for (auto& value : values) {
PerpetualFutures trade(value.payoffType, value.fundingType, value.fundingFreq, cal, dc);
Handle<YieldTermStructure> domCurve(flatRate(today, value.r, dc));
Handle<YieldTermStructure> forCurve(flatRate(today, value.q, dc));
Handle<Quote> spot(ext::make_shared<SimpleQuote>(value.s));
std::vector<Real> fundingTimes = { 0.0 }, fundingRates = { value.k }, interestRateDiffs = { value.iDiff };
ext::shared_ptr<PricingEngine> engine(new DiscountingPerpetualFuturesEngine(
domCurve, forCurve, spot, fundingTimes, fundingRates, interestRateDiffs));
trade.setPricingEngine(engine);
Real calculated = trade.NPV();
// analytic
// for details, refer to
// Perpetual Futures Pricing, Damien Ackerer, Julien Hugonnier, Urban Jermann, 2024
// https://finance.wharton.upenn.edu/~jermann/AHJ-main-10.pdf
Real dt = 0.;
switch (value.fundingFreq.units()) {
case Years:
dt = (Real)value.fundingFreq.length();
break;
case Months:
dt = (Real)value.fundingFreq.length() / 12.;
break;
case Weeks:
dt = (Real)value.fundingFreq.length() * 7. / 365.;
break;
case Days:
dt = (Real)value.fundingFreq.length() / 365.;
break;
case Hours:
dt = (Real)value.fundingFreq.length() / 365. / 24.;
break;
case Minutes:
dt = (Real)value.fundingFreq.length() / 365. / 24. / 60.;
break;
case Seconds:
dt = (Real)value.fundingFreq.length() / 365. / 24. / 60. / 60.;
break;
default:
QL_FAIL("Unknown fundingFrequency unit");
}
Real expected = 0.;
// Discrete time
if (value.fundingFreq.length() > 0) {
if (value.payoffType == PerpetualFutures::Linear) {
if (value.fundingType == PerpetualFutures::FundingWithPreviousSpot) {
// Equation (12) in the above paper
expected =
value.s * (value.k - value.iDiff) * exp(value.q * dt) /
(exp(value.q * dt) - exp(value.r * dt) + value.k * exp(value.q * dt));
} else if (value.fundingType == PerpetualFutures::FundingWithCurrentSpot) {
// at the end of "3 Perpetual futures pricing" in the above paper
expected =
value.s * (value.k - value.iDiff) * exp(value.r * dt) /
(exp(value.q * dt) - exp(value.r * dt) + value.k * exp(value.r * dt));
}
} else if (value.payoffType == PerpetualFutures::Inverse) {
if (value.fundingType == PerpetualFutures::FundingWithPreviousSpot) {
// "Proposition 2" in the above paper
expected =
value.s *
(exp(value.r * dt) - exp(value.q * dt) + value.k * exp(value.r * dt)) /
(value.k - value.iDiff) / exp(value.r * dt);
} else if (value.fundingType == PerpetualFutures::FundingWithCurrentSpot) {
expected =
value.s *
(exp(value.r * dt) - exp(value.q * dt) + value.k * exp(value.q * dt)) /
(value.k - value.iDiff) / exp(value.q * dt);
}
}
} else {
// Continuous time
if (value.payoffType == PerpetualFutures::Linear) {
// "Proposition 3" in the above paper
expected = value.s * (value.k - value.iDiff) / (value.q - value.r + value.k);
} else if (value.payoffType == PerpetualFutures::Inverse) {
// "Proposition 4" in the above paper
expected = value.s * (value.r - value.q + value.k) / (value.k - value.iDiff);
}
}
Real relError = std::fabs(calculated / expected - 1.);
if (relError > value.relTol) {
REPORT_FAILURE("value", value.payoffType, value.fundingType, value.fundingFreq, value.s,
value.r, value.q, value.k, value.iDiff, today, expected, calculated,
relError, value.relTol);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
