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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Roland Lichters
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
<http://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/experimental/credit/nthtodefault.hpp>
#include <ql/experimental/credit/lossdistribution.hpp>
#include <ql/instruments/claim.hpp>
#include <ql/cashflows/fixedratecoupon.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/event.hpp>
namespace QuantLib {
NthToDefault::NthToDefault(
Size n,
const std::vector<Handle<DefaultProbabilityTermStructure> >&
probabilities,
Real recoveryRate,
const Handle<OneFactorCopula>& copula,
Protection::Side side,
Real nominal,
const Schedule& premiumSchedule,
Rate premiumRate,
const DayCounter& dayCounter,
bool settlePremiumAccrual,
const Handle<YieldTermStructure>& yieldTS,
const Period& integrationStepSize,
boost::shared_ptr<Claim> claim)
: n_(n), probabilities_(probabilities), recoveryRate_(recoveryRate),
copula_(copula), side_(side), nominal_(nominal),
premiumSchedule_(premiumSchedule), premiumRate_(premiumRate),
dayCounter_(dayCounter), settlePremiumAccrual_(settlePremiumAccrual),
yieldTS_(yieldTS), integrationStepSize_(integrationStepSize),
claim_(claim) {
premiumLeg_ = FixedRateLeg(premiumSchedule)
.withNotionals(nominal)
.withCouponRates(premiumRate, dayCounter)
.withPaymentAdjustment(Unadjusted);
for (Size i=0; i<probabilities_.size(); i++)
registerWith(probabilities_[i]);
registerWith(copula_);
registerWith(yieldTS_);
if (!claim_)
claim_ = boost::shared_ptr<Claim>(new FaceValueClaim);
registerWith(claim_);
}
bool NthToDefault::isExpired() const {
return detail::simple_event(premiumLeg_.back()->date())
.hasOccurred(yieldTS_->referenceDate());
}
Rate NthToDefault::fairPremium() const {
calculate();
QL_REQUIRE(fairPremium_ != Null<Rate>(),
"fair premium not available");
return fairPremium_;
}
void NthToDefault::setupExpired() const {
Instrument::setupExpired();
fairPremium_ = 0.0;
}
void NthToDefault::performCalculations() const {
QL_REQUIRE(!yieldTS_.empty(), "no yield term structure set");
for (Size i = 0; i < probabilities_.size(); i++) {
QL_REQUIRE(!probabilities_[i].empty(),
"no default term structure set");
if (i > 0) {
QL_REQUIRE(probabilities_[i]->referenceDate() ==
probabilities_[i-1]->referenceDate(),
"basket reference dates do not match");
}
}
errorEstimate_ = Null<Real>();
NPV_ = 0.0;
Real premiumValue = 0.0;
Real accrualValue = 0.0;
Real claimValue = 0.0;
Date d, d0;
for (Size i = 0; i < premiumLeg_.size(); i++) {
boost::shared_ptr<FixedRateCoupon> coupon =
boost::dynamic_pointer_cast<FixedRateCoupon>(premiumLeg_[i]);
Date d = premiumLeg_[i]->date();
if (d > yieldTS_->referenceDate()) {
premiumValue += premiumLeg_[i]->amount()
* yieldTS_->discount(d)
* (1.0 - defaultProbability(d));
if (coupon->accrualStartDate() >= yieldTS_->referenceDate())
d = coupon->accrualStartDate();
else
d = yieldTS_->referenceDate();
// do steps of specified size
d0 = d;
Period stepSize = integrationStepSize_;
Probability defProb0 = defaultProbability(d0);
do {
DiscountFactor disc = yieldTS_->discount(d);
Probability defProb1 = defaultProbability(d);
Probability dcfdd = defProb1 - defProb0;
defProb0 = defProb1;
if (settlePremiumAccrual_)
accrualValue += coupon->accruedAmount(d)*disc*dcfdd;
claimValue -= claim_->amount(d, nominal_, recoveryRate_)
* disc * dcfdd;
d0 = d;
d = d0 + stepSize;
// reduce step size ?
if (stepSize != 1*Days && d > coupon->accrualEndDate()) {
stepSize = 1*Days;
//d = NullCalendar().advance(d0,1,stepSize,Unadjusted);
d = d0 + stepSize;
}
}
while (d <= coupon->accrualEndDate());
}
}
if (side_ == Protection::Buyer) {
premiumValue *= -1;
accrualValue *= -1;
claimValue *= -1;
}
NPV_ = premiumValue + accrualValue + claimValue;
fairPremium_ = -premiumRate_*claimValue/(premiumValue+accrualValue);
}
Probability NthToDefault::defaultProbability(const Date& d) const {
if (d <= probabilities_.front()->referenceDate())
return 0.0;
std::vector<Real> defProb(probabilities_.size());
for (Size j = 0; j < probabilities_.size(); j++)
defProb[j] = probabilities_[j]->defaultProbability(d);
ProbabilityOfAtLeastNEvents op(n_);
return copula_->integral(op, defProb);
}
}
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