/**
* Computes the present value sensitivity to the strike of a CMS cap/floor by replication in SABR
* framework with extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle. The SABR function need to be the Hagan function.
* @return The present value sensitivity to strike.
*/
@Override
public double presentValueStrikeSensitivity(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactor =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
final CMSStrikeIntegrant integrant =
new CMSStrikeIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double factor = discountFactor * integrant.g(forward) / integrant.h(forward);
final double absoluteTolerance = 1.0E-9;
final double relativeTolerance = 1.0E-5;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
final SABRExtrapolationRightFunction sabrExtrapolation =
new SABRExtrapolationRightFunction(
forward, sabrPoint, _cutOffStrike, cmsCapFloor.getFixingTime(), _mu);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(strike, cmsCapFloor.getFixingTime(), cmsCapFloor.isCap());
final double[] kpkpp = integrant.kpkpp(strike);
double firstPart;
double thirdPart;
if (cmsCapFloor.isCap()) {
firstPart = -kpkpp[0] * integrant.bs(strike);
thirdPart = integrator.integrate(integrant, strike, strike + getIntegrationInterval());
} else {
firstPart = 3 * kpkpp[0] * integrant.bs(strike);
thirdPart = integrator.integrate(integrant, 0.0, strike);
}
final double secondPart = integrant.k(strike) * sabrExtrapolation.priceDerivativeStrike(option);
return cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction()
* factor
* (firstPart + secondPart + thirdPart);
}
/**
* Compute the present value of a CMS cap/floor by replication in SABR framework with
* extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle.
* @return The present value.
*/
@Override
public CurrencyAmount presentValue(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
Validate.notNull(cmsCapFloor);
Validate.notNull(sabrData);
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactorTp =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
final CMSIntegrant integrant =
new CMSIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double strike = cmsCapFloor.getStrike();
final double factor = discountFactorTp / integrant.h(forward) * integrant.g(forward);
final double strikePart = factor * integrant.k(strike) * integrant.bs(strike);
final double absoluteTolerance =
1.0 / (factor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
final double relativeTolerance = 1E-10;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
double integralPart;
try {
if (cmsCapFloor.isCap()) {
integralPart =
discountFactorTp
* integrator.integrate(integrant, strike, strike + getIntegrationInterval());
} else {
integralPart = discountFactorTp * integrator.integrate(integrant, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
final double priceCMS =
(strikePart + integralPart)
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
return CurrencyAmount.of(cmsCapFloor.getCurrency(), priceCMS);
}
/**
* Computes the present value of the Physical delivery swaption.
*
* @param swaption The swaption.
* @param hwData The Hull-White parameters and the curves.
* @return The present value.
*/
public CurrencyAmount presentValue(
final SwaptionPhysicalFixedIbor swaption,
final HullWhiteOneFactorPiecewiseConstantDataBundle hwData) {
Validate.notNull(swaption);
Validate.notNull(hwData);
final double expiryTime = swaption.getTimeToExpiry();
final AnnuityPaymentFixed cfe = swaption.getUnderlyingSwap().accept(CFEC, hwData);
final double[] alpha = new double[cfe.getNumberOfPayments()];
final double[] df = new double[cfe.getNumberOfPayments()];
final double[] discountedCashFlow = new double[cfe.getNumberOfPayments()];
for (int loopcf = 0; loopcf < cfe.getNumberOfPayments(); loopcf++) {
alpha[loopcf] =
MODEL.alpha(
hwData.getHullWhiteParameter(),
0.0,
expiryTime,
expiryTime,
cfe.getNthPayment(loopcf).getPaymentTime());
df[loopcf] =
hwData
.getCurve(cfe.getDiscountCurve())
.getDiscountFactor(cfe.getNthPayment(loopcf).getPaymentTime());
discountedCashFlow[loopcf] = df[loopcf] * cfe.getNthPayment(loopcf).getAmount();
}
// Integration
final SwaptionIntegrant integrant = new SwaptionIntegrant(discountedCashFlow, alpha);
final double limit = 10.0;
final double absoluteTolerance = 1.0E-2;
final double relativeTolerance = 1.0E-6;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, NB_INTEGRATION);
double pv = 0.0;
try {
pv =
1.0
/ Math.sqrt(2.0 * Math.PI)
* integrator.integrate(integrant, -limit, limit)
* (swaption.isLong() ? 1.0 : -1.0);
} catch (final Exception e) {
throw new RuntimeException(e);
}
return CurrencyAmount.of(swaption.getCurrency(), pv);
}
/**
* Computes the future price from the curves used to price the underlying bonds and a Hull-White
* one factor model. Computation by numerical integration.
*
* @param futures The future security.
* @param data The curve and Hull-White parameters.
* @return The future price.
*/
public double price(
final BondFuturesSecurity futures, final HullWhiteIssuerProviderInterface data) {
ArgumentChecker.notNull(futures, "Futures");
ArgumentChecker.notNull(data, "Hull-White/Issuer provider");
final Currency ccy = futures.getCurrency();
final LegalEntity issuer = futures.getDeliveryBasketAtDeliveryDate()[0].getIssuerEntity();
final double expiryTime = futures.getNoticeLastTime();
final double deliveryTime = futures.getDeliveryLastTime();
final int nbBonds = futures.getDeliveryBasketAtDeliveryDate().length;
final int[] nbPayments = new int[nbBonds];
final AnnuityPaymentFixed[] cfe = new AnnuityPaymentFixed[nbBonds];
for (int loopb = 0; loopb < nbBonds; loopb++) {
cfe[loopb] =
futures.getDeliveryBasketAtDeliveryDate()[loopb].accept(
CFEC, data.getMulticurveProvider());
nbPayments[loopb] = cfe[loopb].getNumberOfPayments();
final PaymentFixed[] payments = new PaymentFixed[nbPayments[loopb] + 1];
payments[0] =
new PaymentFixed(
ccy,
deliveryTime,
-futures.getDeliveryBasketAtDeliveryDate()[loopb].getAccruedInterest());
System.arraycopy(cfe[loopb].getPayments(), 0, payments, 1, nbPayments[loopb]);
cfe[loopb] = new AnnuityPaymentFixed(payments);
}
final double[][] alpha = new double[nbBonds][];
final double[][] beta = new double[nbBonds][];
final double[][] df = new double[nbBonds][];
final double[][] discountedCashFlow = new double[nbBonds][];
for (int loopb = 0; loopb < nbBonds; loopb++) {
alpha[loopb] = new double[nbPayments[loopb] + 1];
beta[loopb] = new double[nbPayments[loopb] + 1];
df[loopb] = new double[nbPayments[loopb] + 1];
discountedCashFlow[loopb] = new double[nbPayments[loopb] + 1];
for (int loopcf = 0; loopcf < cfe[loopb].getNumberOfPayments(); loopcf++) {
alpha[loopb][loopcf] =
MODEL.alpha(
data.getHullWhiteParameters(),
0.0,
expiryTime,
deliveryTime,
cfe[loopb].getNthPayment(loopcf).getPaymentTime());
beta[loopb][loopcf] =
MODEL.futuresConvexityFactor(
data.getHullWhiteParameters(),
expiryTime,
cfe[loopb].getNthPayment(loopcf).getPaymentTime(),
deliveryTime);
df[loopb][loopcf] =
data.getIssuerProvider()
.getDiscountFactor(issuer, cfe[loopb].getNthPayment(loopcf).getPaymentTime());
discountedCashFlow[loopb][loopcf] =
df[loopb][loopcf]
/ df[loopb][0]
* cfe[loopb].getNthPayment(loopcf).getAmount()
* beta[loopb][loopcf]
/ futures.getConversionFactor()[loopb];
}
}
// Integration
final FuturesIntegrant integrant = new FuturesIntegrant(discountedCashFlow, alpha);
final double limit = 10.0;
final double absoluteTolerance = 1.0E-2;
final double relativeTolerance = 1.0E-6;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, NB_INTEGRATION);
double price = 0.0;
try {
price = 1.0 / Math.sqrt(2.0 * Math.PI) * integrator.integrate(integrant, -limit, limit);
} catch (final Exception e) {
throw new RuntimeException(e);
}
return price;
}
/**
* Computes the present value sensitivity to the SABR parameters of a CMS cap/floor by replication
* in SABR framework with extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle. The SABR function need to be the Hagan function.
* @return The present value sensitivity to SABR parameters.
*/
@Override
public PresentValueSABRSensitivityDataBundle presentValueSABRSensitivity(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactorTp =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
final CMSVegaIntegrant integrantVega =
new CMSVegaIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double factor = discountFactorTp / integrantVega.h(forward) * integrantVega.g(forward);
final SABRExtrapolationRightFunction sabrExtrapolation =
new SABRExtrapolationRightFunction(
forward, sabrPoint, _cutOffStrike, cmsCapFloor.getFixingTime(), _mu);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(strike, cmsCapFloor.getFixingTime(), cmsCapFloor.isCap());
final double factor2 = factor * integrantVega.k(strike);
final double[] strikePartPrice = new double[4];
sabrExtrapolation.priceAdjointSABR(option, strikePartPrice);
for (int loopvega = 0; loopvega < 4; loopvega++) {
strikePartPrice[loopvega] *= factor2;
}
final double absoluteTolerance =
1.0 / (factor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
final double relativeTolerance = 1E-3;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
final double[] integralPart = new double[4];
final double[] totalSensi = new double[4];
for (int loopparameter = 0; loopparameter < 4; loopparameter++) {
integrantVega.setParameterIndex(loopparameter);
try {
if (cmsCapFloor.isCap()) {
integralPart[loopparameter] =
discountFactorTp
* integrator.integrate(integrantVega, strike, strike + getIntegrationInterval());
} else {
integralPart[loopparameter] =
discountFactorTp * integrator.integrate(integrantVega, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
totalSensi[loopparameter] =
(strikePartPrice[loopparameter] + integralPart[loopparameter])
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
}
final PresentValueSABRSensitivityDataBundle sensi = new PresentValueSABRSensitivityDataBundle();
sensi.addAlpha(expiryMaturity, totalSensi[0]);
sensi.addBeta(expiryMaturity, totalSensi[1]);
sensi.addRho(expiryMaturity, totalSensi[2]);
sensi.addNu(expiryMaturity, totalSensi[3]);
return sensi;
}
/**
* Computes the present value sensitivity to the yield curves of a CMS cap/floor by replication in
* the SABR framework with extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle. The SABR function need to be the Hagan function.
* @return The present value sensitivity to curves.
*/
@Override
public InterestRateCurveSensitivity presentValueCurveSensitivity(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
Validate.notNull(cmsCapFloor);
Validate.notNull(sabrData);
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactor =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
// Common
final CMSIntegrant integrantPrice =
new CMSIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final CMSDeltaIntegrant integrantDelta =
new CMSDeltaIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double factor = discountFactor / integrantDelta.h(forward) * integrantDelta.g(forward);
final double absoluteTolerance =
1.0 / (factor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
final double relativeTolerance = 1E-10;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
// Price
final double[] bs = integrantDelta.bsbsp(strike);
@SuppressWarnings("synthetic-access")
final double[] n = integrantDelta.nnp(forward);
final double strikePartPrice = discountFactor * integrantDelta.k(strike) * n[0] * bs[0];
double integralPartPrice;
try {
if (cmsCapFloor.isCap()) {
integralPartPrice =
discountFactor
* integrator.integrate(integrantPrice, strike, strike + getIntegrationInterval());
} else {
integralPartPrice = discountFactor * integrator.integrate(integrantPrice, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
final double price =
(strikePartPrice + integralPartPrice)
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
// Delta
final double strikePart =
discountFactor * integrantDelta.k(strike) * (n[1] * bs[0] + n[0] * bs[1]);
double integralPart;
try {
if (cmsCapFloor.isCap()) {
integralPart =
discountFactor
* integrator.integrate(integrantDelta, strike, strike + getIntegrationInterval());
} else {
integralPart = discountFactor * integrator.integrate(integrantDelta, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
final double deltaS0 =
(strikePart + integralPart)
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
final double deltaPD = price / discountFactor;
final double sensiDF = -cmsCapFloor.getPaymentTime() * discountFactor * deltaPD;
final List<DoublesPair> list = new ArrayList<>();
list.add(new DoublesPair(cmsCapFloor.getPaymentTime(), sensiDF));
final Map<String, List<DoublesPair>> resultMap = new HashMap<>();
resultMap.put(
cmsCapFloor.getUnderlyingSwap().getFixedLeg().getNthPayment(0).getFundingCurveName(), list);
InterestRateCurveSensitivity result = new InterestRateCurveSensitivity(resultMap);
final InterestRateCurveSensitivity forwardDr =
new InterestRateCurveSensitivity(cmsCapFloor.getUnderlyingSwap().accept(PRSC, sabrData));
result = result.plus(forwardDr.multipliedBy(deltaS0));
return result;
}
/**
* Computes the present value of an Ibor cap/floor in arrears by replication based on the paper,
* "Swap and Cap/Floors with Fixing in Arrears or Payment Delay," OpenGamma Quantitative
* Documentation
* http://developers.opengamma.com/quantitative-research/In-Arrears-and-Payment-Delay-Swaps-and-Caps-OpenGamma.pdf
*
* @param cap The cap/floor
* @param curves The curves
* @return The present value
*/
public MultipleCurrencyAmount presentValue(
final CapFloorIbor cap, final MulticurveProviderInterface curves) {
ArgumentChecker.notNull(cap, "The cap/floor shoud not be null");
ArgumentChecker.notNull(curves, "curves");
final Currency ccy = cap.getCurrency();
// Construct a "standard" CapFloorIbor whose paymentTime is set to be fixingPeriodEndTime
CapFloorIbor capStandard =
new CapFloorIbor(
cap.getCurrency(),
cap.getFixingPeriodEndTime(),
cap.getPaymentYearFraction(),
cap.getNotional(),
cap.getFixingTime(),
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor(),
cap.getStrike(),
cap.isCap());
final double forward =
curves.getSimplyCompoundForwardRate(
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor());
final double beta =
(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
final double df =
curves.getDiscountFactor(capStandard.getCurrency(), capStandard.getPaymentTime());
final double strikePart =
(1.0 + cap.getFixingAccrualFactor() * capStandard.getStrike())
* presentValueStandard(
forward,
capStandard.getStrike(),
capStandard.getFixingTime(),
capStandard.isCap(),
df,
capStandard.getNotional(),
capStandard.getPaymentYearFraction());
final InArrearsIntegrant integrant = new InArrearsIntegrant(capStandard, curves);
double integralPart;
try {
if (cap.isCap()) {
double atmVol = _smileFunction.getVolatility(forward);
double upper = forward * Math.exp(6.0 * atmVol * Math.sqrt(cap.getFixingTime()));
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, strike, upper);
double reminder = integrant.evaluate(upper) * upper;
double error = reminder / integralPart;
int count = 0;
while (Math.abs(error) > REL_ERROR && count < MAX_COUNT) {
integralPart += INTEGRATOR.integrate(integrant, upper, 2.0 * upper);
upper *= 2.0;
// The increase of integralPart in the next loop is bounded by reminder
reminder = integrant.evaluate(upper) * upper;
error = reminder / integralPart;
++count;
if (count == MAX_COUNT) {
LOGGER.info(
"Maximum iteration count, "
+ MAX_COUNT
+ ", has been reached. Relative error is greater than "
+ REL_ERROR);
}
}
} else {
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, REL_TOL * strike, strike);
}
} catch (final Exception e) {
throw new MathException(e);
}
integralPart *= 2.0 * cap.getFixingAccrualFactor();
final double pv = (strikePart + integralPart) / beta;
return MultipleCurrencyAmount.of(cap.getCurrency(), pv);
}
/**
* Computes the pv sensitivity of an Ibor cap/floor in arrears
*
* @param cap The cap/floor
* @param curves The curves
* @return The sensitivity
*/
public MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(
final CapFloorIbor cap, final MulticurveProviderInterface curves) {
ArgumentChecker.notNull(cap, "The cap/floor shoud not be null");
ArgumentChecker.notNull(curves, "curves");
final Currency ccy = cap.getCurrency();
// Construct a "standard" CapFloorIbor whose paymentTime is set to be fixingPeriodEndTime
CapFloorIbor capStandard =
new CapFloorIbor(
cap.getCurrency(),
cap.getFixingPeriodEndTime(),
cap.getPaymentYearFraction(),
cap.getNotional(),
cap.getFixingTime(),
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor(),
cap.getStrike(),
cap.isCap());
final double forward =
curves.getSimplyCompoundForwardRate(
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor());
final double beta =
(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
double df = curves.getDiscountFactor(capStandard.getCurrency(), capStandard.getPaymentTime());
double strikePart =
(1.0 + cap.getFixingAccrualFactor() * capStandard.getStrike())
* presentValueStandard(
forward,
capStandard.getStrike(),
capStandard.getFixingTime(),
capStandard.isCap(),
df,
capStandard.getNotional(),
capStandard.getPaymentYearFraction());
double strikePartDelta =
(1.0 + cap.getFixingAccrualFactor() * capStandard.getStrike())
* presentValueDeltaStandard(
forward,
capStandard.getStrike(),
capStandard.getFixingTime(),
capStandard.isCap(),
df,
capStandard.getNotional(),
capStandard.getPaymentYearFraction());
final InArrearsIntegrant integrant = new InArrearsIntegrant(capStandard, curves);
double integralPart;
double upper = 0.0;
try {
if (cap.isCap()) {
double atmVol = _smileFunction.getVolatility(forward);
upper = forward * Math.exp(6.0 * atmVol * Math.sqrt(cap.getFixingTime()));
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, strike, upper);
double reminder = integrant.evaluate(upper) * upper;
double error = reminder / integralPart;
int count = 0;
while (Math.abs(error) > REL_ERROR && count < MAX_COUNT) {
integralPart += INTEGRATOR.integrate(integrant, upper, 2.0 * upper);
upper *= 2.0;
// The increase of integralPart in the next loop is bounded by reminder
reminder = integrant.evaluate(upper) * upper;
error = reminder / integralPart;
++count;
if (count == MAX_COUNT) {
LOGGER.info(
"Maximum iteration count, "
+ MAX_COUNT
+ ", has been reached. Relative error is greater than "
+ REL_ERROR);
}
}
} else {
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, REL_TOL * strike, strike);
}
} catch (final Exception e) {
throw new MathException(e);
}
integralPart *= 2.0 * cap.getFixingAccrualFactor();
double pv = (strikePart + integralPart) / beta;
double betaFwd =
cap.getFixingAccrualFactor()
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
double betaDscStart =
(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
* cap.getFixingPeriodStartTime()
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
double betaDscEnd =
-(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
* cap.getFixingPeriodEndTime()
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
List<DoublesPair> listDiscounting = new ArrayList<>();
double strikePartDsc = -capStandard.getPaymentTime() * strikePart;
double integralPartDsc = -capStandard.getPaymentTime() * integralPart;
listDiscounting.add(
DoublesPair.of(capStandard.getPaymentTime(), (strikePartDsc + integralPartDsc) / beta));
listDiscounting.add(DoublesPair.of(cap.getFixingPeriodStartTime(), -pv * betaDscStart / beta));
listDiscounting.add(DoublesPair.of(cap.getFixingPeriodEndTime(), -pv * betaDscEnd / beta));
Map<String, List<DoublesPair>> mapDsc = new HashMap<>();
mapDsc.put(curves.getName(capStandard.getCurrency()), listDiscounting);
final List<ForwardSensitivity> listForward = new ArrayList<>();
double strikePartFwd = strikePartDelta;
double integralPartFwd = 0.0;
final InArrearsDeltaIntegrant integrantFwd = new InArrearsDeltaIntegrant(capStandard, curves);
try {
if (cap.isCap()) {
double strike = cap.getStrike();
integralPartFwd = INTEGRATOR.integrate(integrantFwd, strike, upper);
} else {
double strike = cap.getStrike();
integralPartFwd = INTEGRATOR.integrate(integrantFwd, REL_TOL * strike, strike);
}
} catch (final Exception e) {
throw new MathException(e);
}
integralPartFwd *= 2.0 * cap.getFixingAccrualFactor();
listForward.add(
new SimplyCompoundedForwardSensitivity(
capStandard.getFixingPeriodStartTime(),
capStandard.getFixingPeriodEndTime(),
capStandard.getFixingAccrualFactor(),
(strikePartFwd + integralPartFwd - pv * betaFwd) / beta));
Map<String, List<ForwardSensitivity>> mapFwd = new HashMap<>();
mapFwd.put(curves.getName(capStandard.getIndex()), listForward);
return MultipleCurrencyMulticurveSensitivity.of(
cap.getCurrency(), MulticurveSensitivity.of(mapDsc, mapFwd));
}