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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Jose Aparicio
Copyright (C) 2014 Peter Caspers
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/cashflows/fixedratecoupon.hpp>
#include <ql/instruments/claim.hpp>
#include <ql/math/interpolations/forwardflatinterpolation.hpp>
#include <ql/pricingengines/credit/isdacdsengine.hpp>
#include <ql/termstructures/credit/flathazardrate.hpp>
#include <ql/termstructures/credit/piecewisedefaultcurve.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/yield/piecewiseyieldcurve.hpp>
#include <ql/time/calendars/weekendsonly.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/optional.hpp>
#include <utility>
namespace QuantLib {
IsdaCdsEngine::IsdaCdsEngine(Handle<DefaultProbabilityTermStructure> probability,
Real recoveryRate,
Handle<YieldTermStructure> discountCurve,
const ext::optional<bool>& includeSettlementDateFlows,
const NumericalFix numericalFix,
const AccrualBias accrualBias,
const ForwardsInCouponPeriod forwardsInCouponPeriod)
: probability_(std::move(probability)), recoveryRate_(recoveryRate),
discountCurve_(std::move(discountCurve)),
includeSettlementDateFlows_(includeSettlementDateFlows), numericalFix_(numericalFix),
accrualBias_(accrualBias), forwardsInCouponPeriod_(forwardsInCouponPeriod) {
registerWith(probability_);
registerWith(discountCurve_);
}
void IsdaCdsEngine::calculate() const {
QL_REQUIRE(numericalFix_ == None || numericalFix_ == Taylor,
"numerical fix must be None or Taylor");
QL_REQUIRE(accrualBias_ == HalfDayBias || accrualBias_ == NoBias,
"accrual bias must be HalfDayBias or NoBias");
QL_REQUIRE(forwardsInCouponPeriod_ == Flat ||
forwardsInCouponPeriod_ == Piecewise,
"forwards in coupon period must be Flat or Piecewise");
// it would be possible to handle the cases which are excluded below,
// but the ISDA engine is not explicitly specified to handle them,
// so we just forbid them too
Actual365Fixed dc;
Actual360 dc1;
Actual360 dc2(true);
Date evalDate = Settings::instance().evaluationDate();
// check if given curves are ISDA compatible
// (the interpolation is checked below)
QL_REQUIRE(!discountCurve_.empty(), "no discount term structure set");
QL_REQUIRE(!probability_.empty(), "no probability term structure set");
QL_REQUIRE(discountCurve_->dayCounter() == dc,
"yield term structure day counter ("
<< discountCurve_->dayCounter()
<< ") should be Act/365(Fixed)");
QL_REQUIRE(probability_->dayCounter() == dc,
"probability term structure day counter ("
<< probability_->dayCounter() << ") should be "
<< "Act/365(Fixed)");
QL_REQUIRE(discountCurve_->referenceDate() == evalDate,
"yield term structure reference date ("
<< discountCurve_->referenceDate()
<< " should be evaluation date (" << evalDate << ")");
QL_REQUIRE(probability_->referenceDate() == evalDate,
"probability term structure reference date ("
<< probability_->referenceDate()
<< " should be evaluation date (" << evalDate << ")");
QL_REQUIRE(arguments_.settlesAccrual,
"ISDA engine not compatible with non accrual paying CDS");
QL_REQUIRE(arguments_.paysAtDefaultTime,
"ISDA engine not compatible with end period payment");
QL_REQUIRE(ext::dynamic_pointer_cast<FaceValueClaim>(arguments_.claim) != nullptr,
"ISDA engine not compatible with non face value claim");
Date maturity = arguments_.maturity;
Date effectiveProtectionStart =
std::max<Date>(arguments_.protectionStart, evalDate + 1);
// collect nodes from both curves and sort them
std::vector<Date> yDates, cDates;
// the calls to dates() below might not trigger bootstrap (because
// they will call the InterpolatedCurve methods, not the ones from
// PiecewiseYieldCurve or PiecewiseDefaultCurve) so we force it here
discountCurve_->discount(0.0);
probability_->defaultProbability(0.0);
if(ext::shared_ptr<InterpolatedDiscountCurve<LogLinear> > castY1 =
ext::dynamic_pointer_cast<
InterpolatedDiscountCurve<LogLinear> >(*discountCurve_)) {
yDates = castY1->dates();
} else if(ext::shared_ptr<InterpolatedForwardCurve<BackwardFlat> >
castY2 = ext::dynamic_pointer_cast<
InterpolatedForwardCurve<BackwardFlat> >(*discountCurve_)) {
yDates = castY2->dates();
} else if(ext::shared_ptr<InterpolatedForwardCurve<ForwardFlat> >
castY3 = ext::dynamic_pointer_cast<
InterpolatedForwardCurve<ForwardFlat> >(*discountCurve_)) {
yDates = castY3->dates();
} else if(ext::shared_ptr<FlatForward> castY4 =
ext::dynamic_pointer_cast<FlatForward>(*discountCurve_)) {
// no dates to extract
} else {
QL_FAIL("Yield curve must be flat forward interpolated");
}
if(ext::shared_ptr<InterpolatedSurvivalProbabilityCurve<LogLinear> >
castC1 = ext::dynamic_pointer_cast<
InterpolatedSurvivalProbabilityCurve<LogLinear> >(
*probability_)) {
cDates = castC1->dates();
} else if(
ext::shared_ptr<InterpolatedHazardRateCurve<BackwardFlat> > castC2 =
ext::dynamic_pointer_cast<
InterpolatedHazardRateCurve<BackwardFlat> >(*probability_)) {
cDates = castC2->dates();
} else if(
ext::shared_ptr<FlatHazardRate> castC3 =
ext::dynamic_pointer_cast<FlatHazardRate>(*probability_)) {
// no dates to extract
} else{
QL_FAIL("Credit curve must be flat forward interpolated");
}
std::vector<Date> nodes;
std::set_union(yDates.begin(), yDates.end(), cDates.begin(), cDates.end(), std::back_inserter(nodes));
if(nodes.empty()){
nodes.push_back(maturity);
}
const Real nFix = (numericalFix_ == None ? 1E-50 : 0.0);
// protection leg pricing (npv is always negative at this stage)
Real protectionNpv = 0.0;
Date d0 = effectiveProtectionStart-1;
Real P0 = discountCurve_->discount(d0);
Real Q0 = probability_->survivalProbability(d0);
Date d1;
auto it =
std::upper_bound(nodes.begin(), nodes.end(), effectiveProtectionStart);
for(;it != nodes.end(); ++it) {
if(*it > maturity) {
d1 = maturity;
it = nodes.end() - 1; //early exit
} else {
d1 = *it;
}
Real P1 = discountCurve_->discount(d1);
Real Q1 = probability_->survivalProbability(d1);
Real fhat = std::log(P0) - std::log(P1);
Real hhat = std::log(Q0) - std::log(Q1);
Real fhphh = fhat + hhat;
if (fhphh < 1E-4 && numericalFix_ == Taylor) {
Real fhphhq = fhphh * fhphh;
protectionNpv +=
P0 * Q0 * hhat * (1.0 - 0.5 * fhphh + 1.0 / 6.0 * fhphhq -
1.0 / 24.0 * fhphhq * fhphh +
1.0 / 120 * fhphhq * fhphhq);
} else {
protectionNpv += hhat / (fhphh + nFix) * (P0 * Q0 - P1 * Q1);
}
d0 = d1;
P0 = P1;
Q0 = Q1;
}
protectionNpv *= arguments_.claim->amount(
Date(), arguments_.notional, recoveryRate_);
results_.defaultLegNPV = protectionNpv;
// premium leg pricing (npv is always positive at this stage)
Real premiumNpv = 0.0, defaultAccrualNpv = 0.0;
for (auto& i : arguments_.leg) {
ext::shared_ptr<FixedRateCoupon> coupon = ext::dynamic_pointer_cast<FixedRateCoupon>(i);
QL_REQUIRE(coupon->dayCounter() == dc ||
coupon->dayCounter() == dc1 ||
coupon->dayCounter() == dc2,
"ISDA engine requires a coupon day counter Act/365Fixed "
<< "or Act/360 (" << coupon->dayCounter() << ")");
// premium coupons
if (!i->hasOccurred(effectiveProtectionStart, includeSettlementDateFlows_)) {
premiumNpv +=
coupon->amount() *
discountCurve_->discount(coupon->date()) *
probability_->survivalProbability(coupon->date()-1);
}
// default accruals
if (!detail::simple_event(coupon->accrualEndDate())
.hasOccurred(effectiveProtectionStart, false)) {
Date start = std::max<Date>(coupon->accrualStartDate(),
effectiveProtectionStart)-1;
Date end = coupon->date()-1;
Real tstart =
discountCurve_->timeFromReference(coupon->accrualStartDate()-1) -
(accrualBias_ == HalfDayBias ? 1.0 / 730.0 : 0.0);
std::vector<Date> localNodes;
localNodes.push_back(start);
//add intermediary nodes, if any
if (forwardsInCouponPeriod_ == Piecewise) {
auto it0 =
std::upper_bound(nodes.begin(), nodes.end(), start);
auto it1 =
std::lower_bound(nodes.begin(), nodes.end(), end);
localNodes.insert(localNodes.end(), it0, it1);
}
localNodes.push_back(end);
Real defaultAccrThisNode = 0.;
auto node = localNodes.begin();
Real t0 = discountCurve_->timeFromReference(*node);
Real P0 = discountCurve_->discount(*node);
Real Q0 = probability_->survivalProbability(*node);
for (++node; node != localNodes.end(); ++node) {
Real t1 = discountCurve_->timeFromReference(*node);
Real P1 = discountCurve_->discount(*node);
Real Q1 = probability_->survivalProbability(*node);
Real fhat = std::log(P0) - std::log(P1);
Real hhat = std::log(Q0) - std::log(Q1);
Real fhphh = fhat + hhat;
if (fhphh < 1E-4 && numericalFix_ == Taylor) {
// see above, terms up to (f+h)^3 seem more than enough,
// what exactly is implemented in the standard isda C
// code ?
Real fhphhq = fhphh * fhphh;
defaultAccrThisNode +=
hhat * P0 * Q0 *
((t0 - tstart) *
(1.0 - 0.5 * fhphh + 1.0 / 6.0 * fhphhq -
1.0 / 24.0 * fhphhq * fhphh) +
(t1 - t0) *
(0.5 - 1.0 / 3.0 * fhphh + 1.0 / 8.0 * fhphhq -
1.0 / 30.0 * fhphhq * fhphh));
} else {
defaultAccrThisNode +=
(hhat / (fhphh + nFix)) *
((t1 - t0) * ((P0 * Q0 - P1 * Q1) / (fhphh + nFix) -
P1 * Q1) +
(t0 - tstart) * (P0 * Q0 - P1 * Q1));
}
t0 = t1;
P0 = P1;
Q0 = Q1;
}
defaultAccrualNpv += defaultAccrThisNode * arguments_.notional *
coupon->rate() * 365. / 360.;
}
}
results_.couponLegNPV = premiumNpv + defaultAccrualNpv;
// upfront flow npv
Real upfPVO1 = 0.0;
results_.upfrontNPV = 0.0;
if (!arguments_.upfrontPayment->hasOccurred(
evalDate, includeSettlementDateFlows_)) {
upfPVO1 =
discountCurve_->discount(arguments_.upfrontPayment->date());
if(arguments_.upfrontPayment->amount() != 0.) {
results_.upfrontNPV = upfPVO1 * arguments_.upfrontPayment->amount();
}
}
results_.accrualRebateNPV = 0.;
// NOLINTNEXTLINE(readability-implicit-bool-conversion)
if (arguments_.accrualRebate && arguments_.accrualRebate->amount() != 0. &&
!arguments_.accrualRebate->hasOccurred(evalDate, includeSettlementDateFlows_)) {
results_.accrualRebateNPV =
discountCurve_->discount(arguments_.accrualRebate->date()) *
arguments_.accrualRebate->amount();
}
Real upfrontSign = 1.0;
switch (arguments_.side) {
case Protection::Seller:
results_.defaultLegNPV *= -1.0;
results_.accrualRebateNPV *= -1.0;
break;
case Protection::Buyer:
results_.couponLegNPV *= -1.0;
results_.upfrontNPV *= -1.0;
upfrontSign = -1.0;
break;
default:
QL_FAIL("unknown protection side");
}
results_.value = results_.defaultLegNPV + results_.couponLegNPV +
results_.upfrontNPV + results_.accrualRebateNPV;
results_.errorEstimate = Null<Real>();
if (results_.couponLegNPV != 0.0) {
results_.fairSpread =
-results_.defaultLegNPV * arguments_.spread /
(results_.couponLegNPV + results_.accrualRebateNPV);
} else {
results_.fairSpread = Null<Rate>();
}
Real upfrontSensitivity = upfPVO1 * arguments_.notional;
if (upfrontSensitivity != 0.0) {
results_.fairUpfront =
-upfrontSign * (results_.defaultLegNPV + results_.couponLegNPV +
results_.accrualRebateNPV) /
upfrontSensitivity;
} else {
results_.fairUpfront = Null<Rate>();
}
static const Rate basisPoint = 1.0e-4;
if (arguments_.spread != 0.0) {
results_.couponLegBPS =
results_.couponLegNPV * basisPoint / arguments_.spread;
} else {
results_.couponLegBPS = Null<Rate>();
}
// NOLINTNEXTLINE(readability-implicit-bool-conversion)
if (arguments_.upfront && *arguments_.upfront != 0.0) {
results_.upfrontBPS =
results_.upfrontNPV * basisPoint / (*arguments_.upfront);
} else {
results_.upfrontBPS = Null<Rate>();
}
}
}
|
