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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011, 2012, 2013, 2023 Andre Miemiec
Copyright (C) 2012 Samuel Tebege
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/cashflows.hpp>
#include <ql/cashflows/couponpricer.hpp>
#include <ql/exercise.hpp>
#include <ql/experimental/swaptions/haganirregularswaptionengine.hpp>
#include <ql/instruments/swaption.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/math/matrixutilities/svd.hpp>
#include <ql/math/solvers1d/bisection.hpp>
#include <ql/math/solvers1d/brent.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/pricingengines/swaption/blackswaptionengine.hpp>
#include <utility>
namespace QuantLib {
//////////////////////////////////////////////////////////////////////////
// Implementation of helper class HaganIrregularSwaptionEngine::Basket //
//////////////////////////////////////////////////////////////////////////
HaganIrregularSwaptionEngine::Basket::Basket(
ext::shared_ptr<IrregularSwap> swap,
Handle<YieldTermStructure> termStructure,
Handle<SwaptionVolatilityStructure> volatilityStructure)
: swap_(std::move(swap)), termStructure_(std::move(termStructure)),
volatilityStructure_(std::move(volatilityStructure)) {
engine_ = ext::shared_ptr<PricingEngine>(new DiscountingSwapEngine(termStructure_));
// store swap npv
swap_->setPricingEngine(engine_);
targetNPV_ = swap_->NPV();
// build standard swaps
const Leg& fixedLeg = swap_->fixedLeg();
const Leg& floatLeg = swap_->floatingLeg();
Leg fixedCFS, floatCFS;
for (Size i = 0; i < fixedLeg.size(); ++i) {
// retrieve fixed rate coupon from fixed leg
ext::shared_ptr<FixedRateCoupon> coupon =
ext::dynamic_pointer_cast<FixedRateCoupon>(fixedLeg[i]);
QL_REQUIRE(coupon, "dynamic cast of fixed leg coupon failed.");
expiries_.push_back(coupon->date());
ext::shared_ptr<FixedRateCoupon> newCpn = ext::make_shared<FixedRateCoupon>(
coupon->date(), 1.0, coupon->rate(), coupon->dayCounter(),
coupon->accrualStartDate(), coupon->accrualEndDate(),
coupon->referencePeriodStart(), coupon->referencePeriodEnd());
fixedCFS.push_back(newCpn);
annuities_.push_back(10000 * CashFlows::bps(fixedCFS, **termStructure_, true));
floatCFS.clear();
for (const auto& j : floatLeg) {
// retrieve ibor coupon from floating leg
ext::shared_ptr<IborCoupon> coupon = ext::dynamic_pointer_cast<IborCoupon>(j);
QL_REQUIRE(coupon, "dynamic cast of float leg coupon failed.");
if (coupon->date() <= expiries_[i]) {
ext::shared_ptr<IborCoupon> newCpn = ext::make_shared<IborCoupon>(
coupon->date(), 1.0, coupon->accrualStartDate(), coupon->accrualEndDate(),
coupon->fixingDays(), coupon->iborIndex(), 1.0, coupon->spread(),
coupon->referencePeriodStart(), coupon->referencePeriodEnd(),
coupon->dayCounter(), coupon->isInArrears());
if (!newCpn->isInArrears())
newCpn->setPricer(
ext::shared_ptr<FloatingRateCouponPricer>(new BlackIborCouponPricer()));
floatCFS.push_back(newCpn);
}
}
Real floatLegNPV = CashFlows::npv(floatCFS, **termStructure_, true);
fairRates_.push_back(floatLegNPV / annuities_[i]);
}
}
// computes a replication of the swap in terms of a basket of vanilla swaps
// by solving a linear system of equation
Array HaganIrregularSwaptionEngine::Basket::compute(Rate lambda) const {
// update members
lambda_ = lambda;
Size n = swap_->fixedLeg().size();
// build linear system of equations
Matrix arr(n, n, 0.0);
Array rhs(n);
// fill the matrix describing the linear system of equations by looping over rows
for (Size r = 0; r < n; ++r) {
ext::shared_ptr<FixedRateCoupon> cpn_r =
ext::dynamic_pointer_cast<FixedRateCoupon>(swap_->fixedLeg()[r]);
QL_REQUIRE(cpn_r, "Cast to fixed rate coupon failed.");
// looping over columns
for (Size c = r; c < n; ++c) {
// set homogenous part of lse
arr[r][c] = (fairRates_[c] + lambda_) * cpn_r->accrualPeriod();
}
// add nominal repayment for i-th swap
arr[r][r] += 1;
}
for (Size r = 0; r < n; ++r) {
ext::shared_ptr<FixedRateCoupon> cpn_r =
ext::dynamic_pointer_cast<FixedRateCoupon>(swap_->fixedLeg()[r]);
// set inhomogenity of lse
Real N_r = cpn_r->nominal();
if (r < n - 1) {
ext::shared_ptr<FixedRateCoupon> cpn_rp1 =
ext::dynamic_pointer_cast<FixedRateCoupon>(swap_->fixedLeg()[r + 1]);
Real N_rp1 = cpn_rp1->nominal();
rhs[r] = N_r * (cpn_r->rate()) * cpn_r->accrualPeriod() + (N_r - N_rp1);
} else {
rhs[r] = N_r * (cpn_r->rate()) * cpn_r->accrualPeriod() + N_r;
}
}
SVD svd(arr);
return svd.solveFor(rhs);
}
Real HaganIrregularSwaptionEngine::Basket::operator()(Rate lambda) const {
Array weights = compute(lambda);
Real defect = -targetNPV_;
for (Size i = 0; i < weights.size(); ++i)
defect -= Integer(swap_->type()) * lambda * weights[i] * annuities_[i];
return defect;
}
// creates a standard swap by deducing its conventions from market data objects
ext::shared_ptr<VanillaSwap> HaganIrregularSwaptionEngine::Basket::component(Size i) const {
ext::shared_ptr<IborCoupon> iborCpn =
ext::dynamic_pointer_cast<IborCoupon>(swap_->floatingLeg()[0]);
QL_REQUIRE(iborCpn, "dynamic cast of float leg coupon failed. Can't find index.");
ext::shared_ptr<IborIndex> iborIndex = iborCpn->iborIndex();
Period dummySwapLength = Period(1, Years);
ext::shared_ptr<VanillaSwap> memberSwap_ =
MakeVanillaSwap(dummySwapLength, iborIndex)
.withType(swap_->type())
.withEffectiveDate(swap_->startDate())
.withTerminationDate(expiries_[i])
.withRule(DateGeneration::Backward)
.withDiscountingTermStructure(termStructure_);
Real stdAnnuity = 10000 * CashFlows::bps(memberSwap_->fixedLeg(), **termStructure_, true);
// compute annuity transformed rate
Rate transformedRate = (fairRates_[i] + lambda_) * annuities_[i] / stdAnnuity;
memberSwap_ = MakeVanillaSwap(dummySwapLength, iborIndex, transformedRate)
.withType(swap_->type())
.withEffectiveDate(swap_->startDate())
.withTerminationDate(expiries_[i])
.withRule(DateGeneration::Backward)
.withDiscountingTermStructure(termStructure_);
return memberSwap_;
}
///////////////////////////////////////////////////////////
// Implementation of class HaganIrregularSwaptionEngine //
///////////////////////////////////////////////////////////
HaganIrregularSwaptionEngine::HaganIrregularSwaptionEngine(
Handle<SwaptionVolatilityStructure> volatilityStructure,
Handle<YieldTermStructure> termStructure)
: termStructure_(std::move(termStructure)),
volatilityStructure_(std::move(volatilityStructure)) {
registerWith(termStructure_);
registerWith(volatilityStructure_);
}
void HaganIrregularSwaptionEngine::calculate() const {
// check exercise type
ext::shared_ptr<Exercise> exercise_ = this->arguments_.exercise;
QL_REQUIRE(exercise_->type() == QuantLib::Exercise::European, "swaption must be european");
// extract the underlying irregular swap
ext::shared_ptr<IrregularSwap> swap_ = this->arguments_.swap;
// Reshuffle spread from float to fixed (, i.e. remove spread from float side by finding the
// adjusted fixed coupon such that the NPV of the swap stays constant).
Leg fixedLeg = swap_->fixedLeg();
Real fxdLgBPS = CashFlows::bps(fixedLeg, **termStructure_, true);
Leg floatLeg = swap_->floatingLeg();
Real fltLgNPV = CashFlows::npv(floatLeg, **termStructure_, true);
Real fltLgBPS = CashFlows::bps(floatLeg, **termStructure_, true);
Leg floatCFS, fixedCFS;
floatCFS.clear();
for (auto& j : floatLeg) {
// retrieve ibor coupon from floating leg
ext::shared_ptr<IborCoupon> coupon = ext::dynamic_pointer_cast<IborCoupon>(j);
QL_REQUIRE(coupon, "dynamic cast of float leg coupon failed.");
ext::shared_ptr<IborCoupon> newCpn = ext::make_shared<IborCoupon>(
coupon->date(), coupon->nominal(), coupon->accrualStartDate(),
coupon->accrualEndDate(), coupon->fixingDays(), coupon->iborIndex(),
coupon->gearing(), 0.0, coupon->referencePeriodStart(),
coupon->referencePeriodEnd(), coupon->dayCounter(), coupon->isInArrears());
if (!newCpn->isInArrears())
newCpn->setPricer(
ext::shared_ptr<FloatingRateCouponPricer>(new BlackIborCouponPricer()));
floatCFS.push_back(newCpn);
}
Real sprdLgNPV = fltLgNPV - CashFlows::npv(floatCFS, **termStructure_, true);
Rate avgSpread = sprdLgNPV / fltLgBPS / 10000;
Rate cpn_adjustment = avgSpread * fltLgBPS / fxdLgBPS;
fixedCFS.clear();
for (auto& i : fixedLeg) {
// retrieve fixed rate coupon from fixed leg
ext::shared_ptr<FixedRateCoupon> coupon = ext::dynamic_pointer_cast<FixedRateCoupon>(i);
QL_REQUIRE(coupon, "dynamic cast of fixed leg coupon failed.");
ext::shared_ptr<FixedRateCoupon> newCpn = ext::make_shared<FixedRateCoupon>(
coupon->date(), coupon->nominal(), coupon->rate() - cpn_adjustment,
coupon->dayCounter(), coupon->accrualStartDate(), coupon->accrualEndDate(),
coupon->referencePeriodStart(), coupon->referencePeriodEnd());
fixedCFS.push_back(newCpn);
}
// this is the irregular swap with spread removed
swap_ = ext::make_shared<IrregularSwap>(arguments_.swap->type(), fixedCFS, floatCFS);
// Sets up the basket by implementing the methodology described in
// P.S.Hagan "Callable Swaps and Bermudan 'Exercise into Swaptions'"
Basket basket(swap_, termStructure_, volatilityStructure_);
///////////////////////////////////////////////////////////////////////////////////////////////////
// find lambda //
///////////////////////////////////////////////////////////////////////////////////////////////////
Bisection s1d;
Rate minLambda = -0.5;
Rate maxLambda = 0.5;
s1d.setMaxEvaluations(10000);
s1d.setLowerBound(minLambda);
s1d.setUpperBound(maxLambda);
s1d.solve(basket, 1.0e-8, 0.01, minLambda, maxLambda);
/////////////////////////////////////////////////////////////////////////////////////////////////
// compute the price of the irreg swaption as the sum of the prices of the regular
// swaptions //
/////////////////////////////////////////////////////////////////////////////////////////////////
results_.value = HKPrice(basket, exercise_);
}
/////////////////////////////////////////////////////////////////////////////////////////
// Computes irregular swaption price according to P.J. Hunt, J.E. Kennedy: //
// "Implied interest rate pricing models", Finance Stochast. 2, 275-293 (1998) //
/////////////////////////////////////////////////////////////////////////////////////////
Real HaganIrregularSwaptionEngine::HKPrice(Basket& basket,
ext::shared_ptr<Exercise>& exercise) const {
// Swaption Engine: assumes that the swaptions exercise date equals the swap start date
QL_REQUIRE((volatilityStructure_->volatilityType() == Normal),
"swaptionEngine: only normal volatility implemented.");
ext::shared_ptr<PricingEngine> swaptionEngine = ext::shared_ptr<PricingEngine>(
new BachelierSwaptionEngine(termStructure_, volatilityStructure_));
// retrieve weights of underlying swaps
Array weights = basket.weights();
Real npv = 0.0;
for (Size i = 0; i < weights.size(); ++i) {
ext::shared_ptr<VanillaSwap> pvSwap_ = basket.component(i);
Swaption swaption = Swaption(pvSwap_, exercise);
swaption.setPricingEngine(swaptionEngine);
npv += weights[i] * swaption.NPV();
}
return npv;
}
}
|
