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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2016 Stefano Fondi
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/averageois/averageoiscouponpricer.hpp>
#include <cmath>
using std::vector;
using std::exp;
using std::pow;
using std::log;
namespace QuantLib {
void ArithmeticAveragedOvernightIndexedCouponPricer::initialize(
const FloatingRateCoupon& coupon) {
coupon_ = dynamic_cast<const OvernightIndexedCoupon*>(&coupon);
QL_ENSURE(coupon_, "wrong coupon type");
}
Rate ArithmeticAveragedOvernightIndexedCouponPricer::swapletRate() const {
ext::shared_ptr<OvernightIndex> index =
ext::dynamic_pointer_cast<OvernightIndex>(coupon_->index());
const vector<Date>& fixingDates = coupon_->fixingDates();
const vector<Time>& dt = coupon_->dt();
Size n = dt.size(),
i = 0;
Real accumulatedRate = 0.0;
// already fixed part
Date today = Settings::instance().evaluationDate();
while (i < n && fixingDates[i] < today) {
// rate must have been fixed
Rate pastFixing = IndexManager::instance().getHistory(
index->name())[fixingDates[i]];
QL_REQUIRE(pastFixing != Null<Real>(),
"Missing " << index->name() <<
" fixing for " << fixingDates[i]);
accumulatedRate += pastFixing*dt[i];
++i;
}
// today is a border case
if (i < n && fixingDates[i] == today) {
// might have been fixed
try {
Rate pastFixing = IndexManager::instance().getHistory(
index->name())[fixingDates[i]];
if (pastFixing != Null<Real>()) {
accumulatedRate += pastFixing*dt[i];
++i;
}
else {
; // fall through and forecast
}
}
catch (Error&) {
; // fall through and forecast
}
}
/* forward part using telescopic property in order
to avoid the evaluation of multiple forward fixings
(approximation proposed by Katsumi Takada)*/
if (byApprox_ && i < n) {
Handle<YieldTermStructure> curve =
index->forwardingTermStructure();
QL_REQUIRE(!curve.empty(),
"null term structure set to this instance of " <<
index->name());
const vector<Date>& dates = coupon_->valueDates();
DiscountFactor startDiscount = curve->discount(dates[i]);
DiscountFactor endDiscount = curve->discount(dates[n]);
accumulatedRate += log(startDiscount / endDiscount) -
convAdj1(curve->timeFromReference(dates[i]),
curve->timeFromReference(dates[n])) -
convAdj2(curve->timeFromReference(dates[i]),
curve->timeFromReference(dates[n]));
}
// otherwise
else if (i < n){
Handle<YieldTermStructure> curve =
index->forwardingTermStructure();
QL_REQUIRE(!curve.empty(),
"null term structure set to this instance of " <<
index->name());
const vector<Date>& dates = coupon_->valueDates();
Time te = curve->timeFromReference(dates[n]);
while (i < n) {
// forcast fixing
Rate forecastFixing = index->fixing(fixingDates[i]);
Time ti1 = curve->timeFromReference(dates[i]);
Time ti2 = curve->timeFromReference(dates[i + 1]);
/*convexity adjustment due to payment dalay of each
overnight fixing, supposing an Hull-White short rate model*/
Real convAdj = exp( 0.5*pow(vol_, 2.0) / pow(mrs_, 3.0)*
(exp(2 * mrs_*ti1) - 1)*
(exp(-mrs_*ti2) - exp(-mrs_*te))*
(exp(-mrs_*ti2) - exp(-mrs_*ti1)) );
accumulatedRate += convAdj*(1 + forecastFixing*dt[i]) - 1;
++i;
}
}
Rate rate = accumulatedRate / coupon_->accrualPeriod();
return coupon_->gearing() * rate + coupon_->spread();
}
Real ArithmeticAveragedOvernightIndexedCouponPricer::convAdj1(
Time ts, Time te) const {
return vol_ * vol_ / (4.0 * pow(mrs_, 3.0)) *
(1.0 - exp(-2.0*mrs_*ts)) *
pow((1.0 - exp(-mrs_*(te - ts))), 2.0);
}
Real ArithmeticAveragedOvernightIndexedCouponPricer::convAdj2(
Time ts, Time te) const {
return vol_ * vol_ / (2.0 * pow(mrs_, 2.0)) * ((te - ts) -
pow(1.0 - exp(-mrs_*(te - ts)), 2.0) / mrs_ -
(1.0 - exp(-2.0*mrs_*(te - ts))) / (2.0 * mrs_));
}
}
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