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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2013 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/pricingengines/swaption/gaussian1dnonstandardswaptionengine.hpp>
#include <ql/rebatedexercise.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/payoff.hpp>
using std::exp;
namespace QuantLib {
Real
Gaussian1dNonstandardSwaptionEngine::underlyingNpv(const Date &expiry,
const Real y) const {
// determine the indices on both legs representing the cashflows that
// are part of the exercise into right
Size fixedIdx =
std::upper_bound(arguments_.fixedResetDates.begin(),
arguments_.fixedResetDates.end(), expiry - 1) -
arguments_.fixedResetDates.begin();
Size floatingIdx =
std::upper_bound(arguments_.floatingResetDates.begin(),
arguments_.floatingResetDates.end(), expiry - 1) -
arguments_.floatingResetDates.begin();
// calculate the npv of these cashflows conditional on y at expiry
Real type = (Real)arguments_.type;
Real npv = 0.0;
for (Size i = fixedIdx; i < arguments_.fixedResetDates.size(); i++) {
npv -=
arguments_.fixedCoupons[i] *
model_->zerobond(arguments_.fixedPayDates[i], expiry, y,
discountCurve_) *
(oas_.empty()
? Real(1.0)
: exp(-oas_->value() *
model_->termStructure()->dayCounter().yearFraction(
expiry, arguments_.fixedPayDates[i])));
}
for (Size i = floatingIdx; i < arguments_.floatingResetDates.size();
i++) {
Real amount;
if (!arguments_.floatingIsRedemptionFlow[i])
amount = (arguments_.floatingGearings[i] *
model_->forwardRate(
arguments_.floatingFixingDates[i], expiry, y,
arguments_.swap->iborIndex()) +
arguments_.floatingSpreads[i]) *
arguments_.floatingAccrualTimes[i] *
arguments_.floatingNominal[i];
else
amount = arguments_.floatingCoupons[i];
npv +=
amount * model_->zerobond(arguments_.floatingPayDates[i],
expiry, y, discountCurve_) *
(oas_.empty()
? Real(1.0)
: exp(-oas_->value() *
model_->termStructure()->dayCounter().yearFraction(
expiry, arguments_.floatingPayDates[i])));
}
return type * npv;
}
Swap::Type Gaussian1dNonstandardSwaptionEngine::underlyingType() const {
return arguments_.swap->type();
}
// NOLINTNEXTLINE(readability-const-return-type)
const Date Gaussian1dNonstandardSwaptionEngine::underlyingLastDate() const {
return arguments_.fixedPayDates.back();
}
// NOLINTNEXTLINE(readability-const-return-type)
const Array Gaussian1dNonstandardSwaptionEngine::initialGuess(const Date &expiry) const {
Size fixedIdx =
std::upper_bound(arguments_.fixedResetDates.begin(),
arguments_.fixedResetDates.end(), expiry - 1) -
arguments_.fixedResetDates.begin();
Array initial(3);
Real nominalSum = 0.0, weightedRate = 0.0, ind = 0.0;
for (Size i = fixedIdx; i < arguments_.fixedResetDates.size(); i++) {
nominalSum += arguments_.fixedNominal[i];
Real rate = arguments_.fixedRate[i];
if (close(rate, 0.0))
rate = 0.03; // this value is at least better than zero
weightedRate += arguments_.fixedNominal[i] * rate;
if (arguments_.fixedNominal[i] > 1E-8) // exclude zero nominal periods
ind += 1.0;
}
Real nominalAvg = nominalSum / ind;
QL_REQUIRE(nominalSum > 0.0,
"sum of nominals on fixed leg must be positive ("
<< nominalSum << ")");
weightedRate /= nominalSum;
initial[0] = nominalAvg;
initial[1] =
model_->termStructure()->timeFromReference(underlyingLastDate()) -
model_->termStructure()->timeFromReference(expiry);
initial[2] = weightedRate;
return initial;
}
void Gaussian1dNonstandardSwaptionEngine::calculate() const {
QL_REQUIRE(arguments_.settlementMethod != Settlement::ParYieldCurve,
"cash settled (ParYieldCurve) swaptions not priced with "
"Gaussian1dNonstandardSwaptionEngine");
Date settlement = model_->termStructure()->referenceDate();
if (arguments_.exercise->dates().back() <=
settlement) { // swaption is expired, possibly generated swap is not
// valued
results_.value = 0.0;
return;
}
ext::shared_ptr<RebatedExercise> rebatedExercise =
ext::dynamic_pointer_cast<RebatedExercise>(arguments_.exercise);
int idx = arguments_.exercise->dates().size() - 1;
int minIdxAlive = static_cast<int>(
std::upper_bound(arguments_.exercise->dates().begin(),
arguments_.exercise->dates().end(), settlement) -
arguments_.exercise->dates().begin());
NonstandardSwap swap = *arguments_.swap;
Option::Type type =
arguments_.type == Swap::Payer ? Option::Call : Option::Put;
Array npv0(2 * integrationPoints_ + 1, 0.0),
npv1(2 * integrationPoints_ + 1, 0.0);
Array z = model_->yGrid(stddevs_, integrationPoints_);
Array p(z.size(), 0.0);
// for probability computation
std::vector<Array> npvp0, npvp1;
if (probabilities_ != None) {
for (int i = 0; i < idx - minIdxAlive + 2; ++i) {
Array npvTmp0(2 * integrationPoints_ + 1, 0.0);
Array npvTmp1(2 * integrationPoints_ + 1, 0.0);
npvp0.push_back(npvTmp0);
npvp1.push_back(npvTmp1);
}
}
// end probability computation
Date expiry1 = Date(), expiry0;
Time expiry1Time = Null<Real>(), expiry0Time;
do {
if (idx == minIdxAlive - 1)
expiry0 = settlement;
else
expiry0 = arguments_.exercise->dates()[idx];
expiry0Time = std::max(
model_->termStructure()->timeFromReference(expiry0), 0.0);
Size j1 =
std::upper_bound(arguments_.fixedResetDates.begin(),
arguments_.fixedResetDates.end(), expiry0 - 1) -
arguments_.fixedResetDates.begin();
Size k1 =
std::upper_bound(arguments_.floatingResetDates.begin(),
arguments_.floatingResetDates.end(), expiry0 - 1) -
arguments_.floatingResetDates.begin();
// todo add openmp support later on (as in gaussian1dswaptionengine)
for (Size k = 0; k < (expiry0 > settlement ? npv0.size() : 1);
k++) {
Real price = 0.0;
if (expiry1Time != Null<Real>()) {
Real zSpreadDf =
oas_.empty() ? Real(1.0)
: std::exp(-oas_->value() *
(expiry1Time - expiry0Time));
Array yg = model_->yGrid(stddevs_, integrationPoints_,
expiry1Time, expiry0Time,
expiry0 > settlement ? z[k] : 0.0);
CubicInterpolation payoff0(
z.begin(), z.end(), npv1.begin(),
CubicInterpolation::Spline, true,
CubicInterpolation::Lagrange, 0.0,
CubicInterpolation::Lagrange, 0.0);
for (Size i = 0; i < yg.size(); i++) {
p[i] = payoff0(yg[i], true);
}
CubicInterpolation payoff1(
z.begin(), z.end(), p.begin(),
CubicInterpolation::Spline, true,
CubicInterpolation::Lagrange, 0.0,
CubicInterpolation::Lagrange, 0.0);
for (Size i = 0; i < z.size() - 1; i++) {
price += Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0, payoff1.cCoefficients()[i],
payoff1.bCoefficients()[i],
payoff1.aCoefficients()[i], p[i], z[i],
z[i], z[i + 1]) *
zSpreadDf;
}
if (extrapolatePayoff_) {
if (flatPayoffExtrapolation_) {
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[z.size() - 2],
z[z.size() - 2], z[z.size() - 1], 100.0) *
zSpreadDf;
price += Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[0], z[0], -100.0,
z[0]) *
zSpreadDf;
} else {
if (type == Option::Call)
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0,
payoff1.cCoefficients()[z.size() - 2],
payoff1.bCoefficients()[z.size() - 2],
payoff1.aCoefficients()[z.size() - 2],
p[z.size() - 2], z[z.size() - 2],
z[z.size() - 1], 100.0) *
zSpreadDf;
if (type == Option::Put)
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0, payoff1.cCoefficients()[0],
payoff1.bCoefficients()[0],
payoff1.aCoefficients()[0], p[0], z[0],
-100.0, z[0]) *
zSpreadDf;
}
}
}
npv0[k] = price;
// for probability computation
if (probabilities_ != None) {
for (Size m = 0; m < npvp0.size(); m++) {
Real price = 0.0;
if (expiry1Time != Null<Real>()) {
Real zSpreadDf =
oas_.empty()
? Real(1.0)
: std::exp(-oas_->value() *
(expiry1Time - expiry0Time));
Array yg = model_->yGrid(
stddevs_, integrationPoints_, expiry1Time,
expiry0Time, expiry0 > settlement ? z[k] : 0.0);
CubicInterpolation payoff0(
z.begin(), z.end(), npvp1[m].begin(),
CubicInterpolation::Spline, true,
CubicInterpolation::Lagrange, 0.0,
CubicInterpolation::Lagrange, 0.0);
for (Size i = 0; i < yg.size(); i++) {
p[i] = payoff0(yg[i], true);
}
CubicInterpolation payoff1(
z.begin(), z.end(), p.begin(),
CubicInterpolation::Spline, true,
CubicInterpolation::Lagrange, 0.0,
CubicInterpolation::Lagrange, 0.0);
for (Size i = 0; i < z.size() - 1; i++) {
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0, payoff1.cCoefficients()[i],
payoff1.bCoefficients()[i],
payoff1.aCoefficients()[i], p[i], z[i],
z[i], z[i + 1]) *
zSpreadDf;
}
if (extrapolatePayoff_) {
if (flatPayoffExtrapolation_) {
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0,
p[z.size() - 2],
z[z.size() - 2],
z[z.size() - 1], 100.0) *
zSpreadDf;
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[0],
z[0], -100.0, z[0]) *
zSpreadDf;
} else {
if (type == Option::Call)
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0,
payoff1.cCoefficients()
[z.size() - 2],
payoff1.bCoefficients()
[z.size() - 2],
payoff1.aCoefficients()
[z.size() - 2],
p[z.size() - 2],
z[z.size() - 2],
z[z.size() - 1], 100.0) *
zSpreadDf;
if (type == Option::Put)
price +=
Gaussian1dModel::gaussianShiftedPolynomialIntegral(
0.0,
payoff1
.cCoefficients()[0],
payoff1
.bCoefficients()[0],
payoff1
.aCoefficients()[0],
p[0], z[0], -100.0,
z[0]) *
zSpreadDf;
}
}
}
npvp0[m][k] = price;
}
}
// end probability computation
if (expiry0 > settlement) {
Real floatingLegNpv = 0.0;
for (Size l = k1; l < arguments_.floatingCoupons.size();
l++) {
Real zSpreadDf =
oas_.empty()
? Real(1.0)
: std::exp(
-oas_->value() *
(model_->termStructure()
->dayCounter()
.yearFraction(
expiry0,
arguments_
.floatingPayDates[l])));
Real amount;
if (arguments_.floatingIsRedemptionFlow[l])
amount = arguments_.floatingCoupons[l];
else
amount = arguments_.floatingNominal[l] *
arguments_.floatingAccrualTimes[l] *
(arguments_.floatingGearings[l] *
model_->forwardRate(
arguments_.floatingFixingDates[l],
expiry0, z[k],
arguments_.swap->iborIndex()) +
arguments_.floatingSpreads[l]);
floatingLegNpv +=
amount *
model_->zerobond(arguments_.floatingPayDates[l],
expiry0, z[k], discountCurve_) *
zSpreadDf;
}
Real fixedLegNpv = 0.0;
for (Size l = j1; l < arguments_.fixedCoupons.size(); l++) {
Real zSpreadDf =
oas_.empty()
? Real(1.0)
: std::exp(
-oas_->value() *
(model_->termStructure()
->dayCounter()
.yearFraction(
expiry0,
arguments_.fixedPayDates[l])));
fixedLegNpv +=
arguments_.fixedCoupons[l] *
model_->zerobond(arguments_.fixedPayDates[l],
expiry0, z[k], discountCurve_) *
zSpreadDf;
}
Real rebate = 0.0;
Real zSpreadDf = 1.0;
Date rebateDate = expiry0;
if (rebatedExercise != nullptr) {
rebate = rebatedExercise->rebate(idx);
rebateDate = rebatedExercise->rebatePaymentDate(idx);
zSpreadDf =
oas_.empty()
? Real(1.0)
: std::exp(
-oas_->value() *
(model_->termStructure()
->dayCounter()
.yearFraction(expiry0, rebateDate)));
}
Real exerciseValue =
((type == Option::Call ? 1.0 : -1.0) *
(floatingLegNpv - fixedLegNpv) +
rebate * model_->zerobond(rebateDate, expiry0, z[k],
discountCurve_) *
zSpreadDf) /
model_->numeraire(expiry0Time, z[k], discountCurve_);
// for probability computation
if (probabilities_ != None) {
if (idx == static_cast<int>(
arguments_.exercise->dates().size()) -
1) // if true we are at the latest date,
// so we init
// the no call probability
npvp0.back()[k] =
probabilities_ == Naive
? Real(1.0)
: 1.0 / (model_->zerobond(expiry0Time, 0.0,
0.0,
discountCurve_) *
model_->numeraire(expiry0, z[k],
discountCurve_));
if (exerciseValue >= npv0[k]) {
npvp0[idx - minIdxAlive][k] =
probabilities_ == Naive
? Real(1.0)
: 1.0 /
(model_->zerobond(expiry0Time, 0.0,
0.0,
discountCurve_) *
model_->numeraire(expiry0Time, z[k],
discountCurve_));
for (Size ii = idx - minIdxAlive + 1;
ii < npvp0.size(); ii++)
npvp0[ii][k] = 0.0;
}
}
// end probability computation
npv0[k] = std::max(npv0[k], exerciseValue);
}
}
npv1.swap(npv0);
// for probability computation
if (probabilities_ != None) {
for (Size i = 0; i < npvp0.size(); i++)
npvp1[i].swap(npvp0[i]);
}
// end probability computation
expiry1 = expiry0;
expiry1Time = expiry0Time;
} while (--idx >= minIdxAlive - 1);
results_.value = npv1[0] * model_->numeraire(0.0, 0.0, discountCurve_);
// for probability computation
if (probabilities_ != None) {
std::vector<Real> prob(npvp0.size());
for (Size i = 0; i < npvp0.size(); i++) {
prob[i] = npvp1[i][0] *
(probabilities_ == Naive
? 1.0
: model_->numeraire(0.0, 0.0, discountCurve_));
}
results_.additionalResults["probabilities"] = prob;
}
// end probability computation
}
}
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