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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2018 Sebastian Schlenkrich
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.
*/
/*! \file tenorswaptionvts.cpp
\brief swaption volatility term structure based on volatility transformation
*/
#include <ql/experimental/basismodels/tenorswaptionvts.hpp>
#include <ql/experimental/basismodels/swaptioncfs.hpp>
#include <ql/instruments/vanillaswap.hpp>
#include <ql/exercise.hpp>
#include <ql/indexes/iborindex.hpp>
#include <ql/math/rounding.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/time/dategenerationrule.hpp>
namespace QuantLib {
TenorSwaptionVTS::TenorSwaptionSmileSection::TenorSwaptionSmileSection(
const TenorSwaptionVTS& volTS, Time optionTime, Time swapLength)
: SmileSection(optionTime, volTS.baseVTS_->dayCounter(), Normal, 0.0) {
baseSmileSection_ = volTS.baseVTS_->smileSection(optionTime, swapLength, true);
// first we need the swap start and end date
Real oneDayAsYear =
volTS.dayCounter().yearFraction(volTS.referenceDate(), volTS.referenceDate() + 1);
Date exerciseDate =
volTS.referenceDate() + ((BigInteger)ClosestRounding(0)(optionTime / oneDayAsYear));
Date effectiveDate = volTS.baseIndex_->fixingCalendar().advance(
exerciseDate, volTS.baseIndex_->fixingDays() * Days);
Date maturityDate = volTS.baseIndex_->fixingCalendar().advance(
effectiveDate, ((BigInteger)swapLength * 12.0) * Months, Unadjusted, false);
// now we can set up the schedules
Schedule baseFixedSchedule(effectiveDate, maturityDate, volTS.baseFixedFreq_,
volTS.baseIndex_->fixingCalendar(), ModifiedFollowing,
Unadjusted, DateGeneration::Backward, false);
Schedule finlFixedSchedule(effectiveDate, maturityDate, volTS.targFixedFreq_,
volTS.targIndex_->fixingCalendar(), ModifiedFollowing,
Unadjusted, DateGeneration::Backward, false);
Schedule baseFloatSchedule(effectiveDate, maturityDate, volTS.baseIndex_->tenor(),
volTS.baseIndex_->fixingCalendar(), ModifiedFollowing,
Unadjusted, DateGeneration::Backward, false);
Schedule targFloatSchedule(effectiveDate, maturityDate, volTS.targIndex_->tenor(),
volTS.baseIndex_->fixingCalendar(), ModifiedFollowing,
Unadjusted, DateGeneration::Backward, false);
// and swaps
auto baseSwap = ext::make_shared<VanillaSwap>(
Swap::Payer, 1.0, baseFixedSchedule, 1.0, volTS.baseFixedDC_, baseFloatSchedule,
volTS.baseIndex_, 0.0, volTS.baseIndex_->dayCounter());
auto targSwap = ext::make_shared<VanillaSwap>(
Swap::Payer, 1.0, baseFixedSchedule, 1.0, volTS.baseFixedDC_, targFloatSchedule,
volTS.targIndex_, 0.0, volTS.targIndex_->dayCounter());
auto finlSwap = ext::make_shared<VanillaSwap>(
Swap::Payer, 1.0, finlFixedSchedule, 1.0, volTS.targFixedDC_, targFloatSchedule,
volTS.targIndex_, 0.0, volTS.targIndex_->dayCounter());
// adding engines
baseSwap->setPricingEngine(
ext::shared_ptr<PricingEngine>(new DiscountingSwapEngine(volTS.discountCurve_)));
targSwap->setPricingEngine(
ext::shared_ptr<PricingEngine>(new DiscountingSwapEngine(volTS.discountCurve_)));
finlSwap->setPricingEngine(
ext::shared_ptr<PricingEngine>(new DiscountingSwapEngine(volTS.discountCurve_)));
// swap rates
swapRateBase_ = baseSwap->fairRate();
swapRateTarg_ = targSwap->fairRate();
swapRateFinl_ = finlSwap->fairRate();
SwaptionCashFlows cfs(
ext::make_shared<Swaption>(
baseSwap, ext::shared_ptr<Exercise>(new EuropeanExercise(exerciseDate))),
volTS.discountCurve_);
SwaptionCashFlows cf2(
ext::make_shared<Swaption>(
targSwap, ext::shared_ptr<Exercise>(new EuropeanExercise(exerciseDate))),
volTS.discountCurve_);
// calculate affine TSR model u and v
// Sum tau_j (fixed leg)
Real sumTauj = 0.0;
for (Real k : cfs.annuityWeights())
sumTauj += k;
// Sum tau_j (T_M - T_j) (fixed leg)
Real sumTaujDeltaT = 0.0;
for (Size k = 0; k < cfs.annuityWeights().size(); ++k)
sumTaujDeltaT +=
cfs.annuityWeights()[k] * (cfs.fixedTimes().back() - cfs.fixedTimes()[k]);
// Sum w_i (float leg)
Real sumWi = 0.0;
for (Real k : cfs.floatWeights())
sumWi += k;
// Sum w_i (T_N - T_i) (float leg)
Real sumWiDeltaT = 0.0;
for (Size k = 0; k < cfs.floatWeights().size(); ++k)
sumWiDeltaT += cfs.floatWeights()[k] * (cfs.floatTimes().back() - cfs.floatTimes()[k]);
// assemble u, v and a(T_p)
Real den = sumTaujDeltaT * sumWi - sumWiDeltaT * sumTauj;
Real u = -sumTauj / den;
Real v = sumTaujDeltaT / den;
Actual365Fixed dc;
// a(T_p) = u (T_p - T_N) + v
Real T_N = cfs.fixedTimes().back();
Real sumBase = 0.0;
Real sumTarg = 0.0;
// we skip the first and last weight as they represent the notional flows
for (Size k = 1; k < cfs.floatWeights().size() - 1; ++k)
sumBase += cfs.floatWeights()[k] * (u * (T_N - cfs.floatTimes()[k]) + v);
for (Size k = 1; k < cf2.floatWeights().size() - 1; ++k)
sumTarg += cf2.floatWeights()[k] * (u * (T_N - cf2.floatTimes()[k]) + v);
lambda_ = sumTarg - sumBase;
// Annuity scaling
annuityScaling_ = targSwap->fixedLegBPS() / finlSwap->fixedLegBPS();
}
Volatility TenorSwaptionVTS::TenorSwaptionSmileSection::volatilityImpl(Rate strike) const {
Real strikeBase = (strike - (swapRateTarg_ - (1.0 + lambda_) * swapRateBase_)) /
(1.0 + lambda_) / annuityScaling_;
Real volBase = baseSmileSection_->volatility(strikeBase, Normal, 0.0);
Real volTarg = annuityScaling_ * (1.0 + lambda_) * volBase;
return volTarg;
}
}
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