void Gaussian1dNonstandardSwaptionEngine::calculate() const {
QL_REQUIRE(arguments_.settlementType == Settlement::Physical,
"cash-settled swaptions not yet implemented ...");
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;
}
boost::shared_ptr<RebatedExercise> rebatedExercise =
boost::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 == VanillaSwap::Payer ? Option::Call : Option::Put;
Schedule schedule = swap.fixedSchedule();
Schedule floatSchedule = swap.floatingSchedule();
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 (Size i = 0; i < static_cast<Size>(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 probabkility computation
Date expiry1 = Null<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(schedule.dates().begin(),
schedule.dates().end(), expiry0 - 1) -
schedule.dates().begin();
Size k1 =
std::upper_bound(floatSchedule.dates().begin(),
floatSchedule.dates().end(), expiry0 - 1) -
floatSchedule.dates().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() ? 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 += model_->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 +=
model_->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 += model_->gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[0], z[0], -100.0,
z[0]) *
zSpreadDf;
} else {
if (type == Option::Call)
price +=
model_->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 +=
model_->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()
? 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 +=
model_->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 +=
model_
->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 +=
model_
->gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[0],
z[0], -100.0, z[0]) *
zSpreadDf;
} else {
if (type == Option::Call)
price +=
model_
->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 +=
model_
->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()
? 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()
? 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 != NULL) {
rebate = rebatedExercise->rebate(idx);
rebateDate = rebatedExercise->rebatePaymentDate(idx);
zSpreadDf =
oas_.empty()
? 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
? 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
? 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
}
void Gaussian1dSwaptionEngine::calculate() const {
QL_REQUIRE(arguments_.settlementType == Settlement::Physical,
"cash-settled swaptions not yet implemented ...");
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;
}
int idx = static_cast<int>(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());
VanillaSwap swap = *arguments_.swap;
Option::Type type =
arguments_.type == VanillaSwap::Payer ? Option::Call : Option::Put;
Schedule fixedSchedule = swap.fixedSchedule();
Schedule floatSchedule = swap.floatingSchedule();
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);
Date expiry1 = Null<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(fixedSchedule.dates().begin(),
fixedSchedule.dates().end(), expiry0 - 1) -
fixedSchedule.dates().begin();
Size k1 =
std::upper_bound(floatSchedule.dates().begin(),
floatSchedule.dates().end(), expiry0 - 1) -
floatSchedule.dates().begin();
// a lazy object is not thread safe, neither is the caching
// in gsrprocess. therefore we trigger computations here such
// that neither lazy object recalculation nor write access
// during caching occurs in the parallized loop below.
// this is known to work for the gsr and markov functional
// model implementations of Gaussian1dModel
#ifdef _OPENMP
if (expiry0 > settlement) {
for (Size l = k1; l < arguments_.floatingCoupons.size(); l++) {
model_->forwardRate(arguments_.floatingFixingDates[l],
expiry0, 0.0,
arguments_.swap->iborIndex());
model_->zerobond(arguments_.floatingPayDates[l], expiry0,
0.0, discountCurve_);
}
for (Size l = j1; l < arguments_.fixedCoupons.size(); l++) {
model_->zerobond(arguments_.fixedPayDates[l], expiry0, 0.0,
discountCurve_);
}
model_->numeraire(expiry0Time, 0.0, discountCurve_);
}
#endif
#pragma omp parallel for default(shared) firstprivate(p) if(expiry0>settlement)
for (Size k = 0; k < (expiry0 > settlement ? npv0.size() : 1);
k++) {
Real price = 0.0;
if (expiry1Time != Null<Real>()) {
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 += model_->gaussianShiftedPolynomialIntegral(
0.0, payoff1.cCoefficients()[i],
payoff1.bCoefficients()[i],
payoff1.aCoefficients()[i], p[i], z[i], z[i],
z[i + 1]);
}
if (extrapolatePayoff_) {
if (flatPayoffExtrapolation_) {
price += model_->gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[z.size() - 2],
z[z.size() - 2], z[z.size() - 1], 100.0);
price += model_->gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[0], z[0], -100.0, z[0]);
} else {
if (type == Option::Call)
price +=
model_->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);
if (type == Option::Put)
price +=
model_->gaussianShiftedPolynomialIntegral(
0.0, payoff1.cCoefficients()[0],
payoff1.bCoefficients()[0],
payoff1.aCoefficients()[0], p[0], z[0],
-100.0, z[0]);
}
}
}
npv0[k] = price;
if (expiry0 > settlement) {
Real floatingLegNpv = 0.0;
for (Size l = k1; l < arguments_.floatingCoupons.size();
l++) {
floatingLegNpv +=
arguments_.nominal *
arguments_.floatingAccrualTimes[l] *
(arguments_.floatingSpreads[l] +
model_->forwardRate(
arguments_.floatingFixingDates[l], expiry0,
z[k], arguments_.swap->iborIndex())) *
model_->zerobond(arguments_.floatingPayDates[l],
expiry0, z[k], discountCurve_);
}
Real fixedLegNpv = 0.0;
for (Size l = j1; l < arguments_.fixedCoupons.size(); l++) {
fixedLegNpv +=
arguments_.fixedCoupons[l] *
model_->zerobond(arguments_.fixedPayDates[l],
expiry0, z[k], discountCurve_);
}
npv0[k] = std::max(npv0[k],
(type == Option::Call ? 1.0 : -1.0) *
(floatingLegNpv - fixedLegNpv) /
model_->numeraire(expiry0Time, z[k],
discountCurve_));
}
}
npv1.swap(npv0);
expiry1 = expiry0;
expiry1Time = expiry0Time;
} while (--idx >= minIdxAlive - 1);
results_.value = npv1[0] * model_->numeraire(0.0, 0.0, discountCurve_);
}