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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 <ql/math/integrals/trapezoidintegral.hpp>
#include <ql/math/interpolations/backwardflatinterpolation.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/pricingengines/futures/discountingperpetualfuturesengine.hpp>
#include <ql/time/daycounters/yearfractiontodate.hpp>
#include <ql/settings.hpp>
namespace QuantLib {
DiscountingPerpetualFuturesEngine::DiscountingPerpetualFuturesEngine(
const Handle<YieldTermStructure>& domesticDiscountCurve,
const Handle<YieldTermStructure>& foreignDiscountCurve,
const Handle<Quote>& assetSpot,
const std::vector<Time>& fundingTimes,
const std::vector<Rate>& fundingRates,
const std::vector<Spread>& interestRateDiffs,
const DiscountingPerpetualFuturesEngine::InterpolationType fundingInterpType,
const Real maxT)
: domesticDiscountCurve_(domesticDiscountCurve),
foreignDiscountCurve_(foreignDiscountCurve), assetSpot_(assetSpot),
fundingTimes_(fundingTimes), fundingRates_(fundingRates),
interestRateDiffs_(interestRateDiffs), fundingInterpType_(fundingInterpType), maxT_(maxT) {
registerWith(domesticDiscountCurve_);
registerWith(foreignDiscountCurve_);
registerWith(assetSpot_);
QL_REQUIRE(!fundingTimes_.empty(), "fundingTimes is empty");
QL_REQUIRE(!fundingRates_.empty(), "fundingRates is empty");
QL_REQUIRE(!interestRateDiffs_.empty(), "interestRateDiffs is empty");
QL_REQUIRE(fundingTimes_.size() == fundingRates_.size(),
"fundingTimes and fundingRates must have the same size.");
QL_REQUIRE(fundingTimes_.size() == interestRateDiffs_.size(),
"fundingTimes and interestRateDiffs must have the same size.");
}
void DiscountingPerpetualFuturesEngine::calculate() const {
QL_REQUIRE(!domesticDiscountCurve_.empty(),
"domestic discounting term structure handle is empty");
QL_REQUIRE(!foreignDiscountCurve_.empty(),
"foreign discounting term structure handle is empty");
QL_REQUIRE(!assetSpot_.empty(), "asset spot handle is empty");
results_.value = 0.0;
results_.errorEstimate = Null<Real>();
QL_REQUIRE(
arguments_.payoffType == PerpetualFutures::Linear ||
arguments_.payoffType == PerpetualFutures::Inverse,
"Only Linear and Inverse payoffs are supported in DiscountingPerpetualFuturesEngine");
// Linear payoff <--> Inverse payoff:
// 1. exchange domestic and foreign curves
// 2. future price: f <--> 1/f
auto effDomCurve = arguments_.payoffType == PerpetualFutures::Linear ?
domesticDiscountCurve_ : foreignDiscountCurve_;
auto effForCurve = arguments_.payoffType == PerpetualFutures::Linear ?
foreignDiscountCurve_ : domesticDiscountCurve_;
Period fundingFreq = arguments_.fundingFrequency;
Date refDate = Settings::instance().evaluationDate();
DayCounter dc = arguments_.dc;
Calendar cal = arguments_.cal;
Interpolation fundingRateInterp =
DiscountingPerpetualFuturesEngine::selectInterpolation(fundingTimes_, fundingRates_);
fundingRateInterp.enableExtrapolation();
QL_REQUIRE(fundingRateInterp(fundingRateInterp.xMax()) > 0,
"fundingRate at max time is negative. Because the last funding rate is "
"flatly extrapolated, integral diverges.");
Interpolation interestRateDiffInterp =
DiscountingPerpetualFuturesEngine::selectInterpolation(fundingTimes_,
interestRateDiffs_);
interestRateDiffInterp.enableExtrapolation();
Real factor = 0.;
if (fundingFreq.length() > 0) {
// discrete-time case
std::vector<Real> timeGrid;
Real tGrid = 0.;
while (tGrid < maxT_) {
timeGrid.push_back(tGrid);
Real tUnit = 0.;
Date date = yearFractionToDate(dc, refDate, tGrid);
Real daysInYear = dc.dayCount(Date(1, January, date.year()), Date(1, January, date.year()+1));
switch (fundingFreq.units()) {
case Years:
tGrid += fundingFreq.length();
break;
case Months:
tUnit = 1. / 12.;
tGrid += tUnit * fundingFreq.length();
break;
case Weeks:
case Days:
tGrid = dc.yearFraction(refDate, cal.advance(date, fundingFreq));
break;
case Hours:
tUnit = 1. / daysInYear / 24.;
tGrid += tUnit * fundingFreq.length();
break;
case Minutes:
tUnit = 1. / daysInYear / 24. / 60.;
tGrid += tUnit * fundingFreq.length();
break;
case Seconds:
tUnit = 1. / daysInYear / 24. / 60. / 60.;
tGrid += tUnit * fundingFreq.length();
break;
case Milliseconds:
tUnit = 1. / daysInYear / 24. / 60. / 60. / 1000.;
tGrid += tUnit * fundingFreq.length();
break;
case Microseconds:
tUnit = 1. / daysInYear / 24. / 60. / 60. / 1000. / 1000.;
tGrid += tUnit * fundingFreq.length();
break;
default:
QL_FAIL("Unknown unit in fundingFrequency");
}
}
std::vector<Rate> fundingRateGrid(timeGrid.size());
std::vector<Spread> interestRateDiffGrid(timeGrid.size());
for (Size i = 0; i < timeGrid.size(); ++i) {
Real time = timeGrid[i];
fundingRateGrid[i] = fundingRateInterp(time);
interestRateDiffGrid[i] = interestRateDiffInterp(time);
}
if (arguments_.fundingType == PerpetualFutures::FundingWithCurrentSpot) {
Real ratio = 1.;
Size i;
for (i = 0; i < timeGrid.size() - 1; ++i) {
Real time = timeGrid[i];
Real nextTime = timeGrid[i + 1];
ratio = effForCurve->discount(nextTime) / effForCurve->discount(time)
/ effDomCurve->discount(nextTime) * effDomCurve->discount(time);
fundingRateGrid[i] *= ratio;
interestRateDiffGrid[i] *= ratio;
}
// for i = timeGrid.size() - 1
fundingRateGrid[i] *= ratio;
interestRateDiffGrid[i] *= ratio;
}
auto productIRDiff = [timeGrid, fundingRateGrid](Size i) {
Real ret = 1.;
for (Size j = 0; j <= i; ++j) {
ret /= 1. + fundingRateGrid[j];
}
return ret;
};
Real sum = 0.;
std::vector<Real> df_dom, df_for;
for (Size i = 0; i < timeGrid.size() - 1; ++i) {
Real time = timeGrid[i];
sum += productIRDiff(i) * (fundingRateGrid[i] - interestRateDiffGrid[i])
* effForCurve->discount(time) / effDomCurve->discount(time);
df_dom.push_back(effDomCurve->discount(time));
df_for.push_back(effForCurve->discount(time));
}
Size iLast = timeGrid.size() - 1;
Real timeLast = timeGrid[iLast];
Real productIRDiffLast = productIRDiff(iLast);
Real fundingRateGridLast = fundingRateGrid[iLast];
Real interestRateDiffGridLast = interestRateDiffGrid[iLast];
Real domRateLast =
effDomCurve->forwardRate(timeLast, timeLast, Continuous, NoFrequency).rate();
Real forRateLast =
effForCurve->forwardRate(timeLast, timeLast, Continuous, NoFrequency).rate();
// for t > maxT_, assume flat extrapolation on all rates
Real lastTerm = productIRDiffLast
* (fundingRateGridLast - interestRateDiffGridLast)
* effForCurve->discount(timeLast) / effDomCurve->discount(timeLast);
Real timeStep = (timeGrid.back() - timeGrid.front()) / (timeGrid.size() - 1);
Real ratio =
1. / (1. + fundingRateGridLast) * exp(-timeStep * (forRateLast - domRateLast));
sum += lastTerm / (1. - ratio);
factor = sum;
} else {
// continuous-time case
TrapezoidIntegral<Default> integrator(1.e-6, 30);
Real fundingRateXMax = fundingRateInterp.xMax();
auto expIRDiff = [&fundingRateInterp, &integrator, fundingRateXMax](Real s) -> Real {
if (s < fundingRateXMax) {
return exp(-integrator(fundingRateInterp, 0., s));
} else {
return exp(-integrator(fundingRateInterp, 0., fundingRateXMax) -
fundingRateInterp(fundingRateXMax) * (s - fundingRateXMax));
}
};
auto timeIntegrand = [fundingRateInterp, interestRateDiffInterp, integrator, expIRDiff,
effDomCurve, effForCurve](Real s) -> Real {
return (fundingRateInterp(s) - interestRateDiffInterp(s)) * expIRDiff(s)
* effForCurve->discount(s) / effDomCurve->discount(s);
};
factor = integrator(timeIntegrand, 0., maxT_);
// for t > maxT_, assume flat extrapolaiton on all rates
Real fundingRateLast = fundingRateInterp(maxT_);
Real interestRateDiffLast = interestRateDiffInterp(maxT_);
Real expIRDiff_last = expIRDiff(maxT_);
Real domRateLast =
effDomCurve->forwardRate(maxT_, maxT_, Continuous, NoFrequency).rate();
Real forRateLast =
effForCurve->forwardRate(maxT_, maxT_, Continuous, NoFrequency).rate();
Real ratio = fundingRateLast + forRateLast - domRateLast;
factor += (fundingRateLast - interestRateDiffLast) * expIRDiff_last *
effForCurve->discount(maxT_) / effDomCurve->discount(maxT_) / ratio;
}
if (arguments_.payoffType == PerpetualFutures::Linear) {
results_.value = assetSpot_->value() * factor;
} else {
results_.value = assetSpot_->value() / factor;
}
}
Interpolation
DiscountingPerpetualFuturesEngine::selectInterpolation(const std::vector<Time>& times,
const std::vector<Real>& values) const {
Interpolation interpolator;
switch (fundingInterpType_) {
case Linear:
interpolator = LinearInterpolation(times.begin(), times.end(), values.begin());
break;
case PiecewiseConstant:
interpolator =
BackwardFlatInterpolation(times.begin(), times.end(), values.begin());
break;
case CubicSpline:
interpolator = CubicNaturalSpline(times.begin(), times.end(), values.begin());
break;
default:
QL_FAIL("Unknown interpolation type");
}
return interpolator;
}
}
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