/**
* 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 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);
}
@Test
/** Tests payer/receiver/swap parity. */
public void presentValueCurveSensitivityPayerReceiverParityExplicit() {
final MultipleCurrencyMulticurveSensitivity pvhwsReceiverLong =
METHOD_HW.presentValueCurveSensitivity(SWAPTION_LONG_RECEIVER, HW_MULTICURVES);
final MultipleCurrencyMulticurveSensitivity pvhwsPayerShort =
METHOD_HW.presentValueCurveSensitivity(SWAPTION_SHORT_PAYER, HW_MULTICURVES);
final MultipleCurrencyMulticurveSensitivity pvSwap = SWAP_RECEIVER.accept(PVCSDC, MULTICURVES);
AssertSensivityObjects.assertEquals(
"Swaption physical - Hull-White - presentValueCurveSensitivity - payer/receiver/swap parity",
pvSwap.cleaned(TOLERANCE_PV_DELTA),
pvhwsReceiverLong.plus(pvhwsPayerShort).cleaned(TOLERANCE_PV_DELTA),
TOLERANCE_PV_DELTA);
}
@Test
/** Tests payer/receiver/swap parity. */
public void payerReceiverParityExplicit() {
final MultipleCurrencyAmount pvReceiverLong =
METHOD_HW.presentValue(SWAPTION_LONG_RECEIVER, HW_MULTICURVES);
final MultipleCurrencyAmount pvPayerShort =
METHOD_HW.presentValue(SWAPTION_SHORT_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvSwap = SWAP_RECEIVER.accept(PVDC, MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - present value - payer/receiver/swap parity",
pvReceiverLong.getAmount(EUR) + pvPayerShort.getAmount(EUR),
pvSwap.getAmount(EUR),
TOLERANCE_PV);
}
@Test
/** Approximation analysis. */
public void presentValueApproximationAnalysis() {
final NormalImpliedVolatilityFormula implied = new NormalImpliedVolatilityFormula();
final int nbStrike = 20;
final double[] pvExplicit = new double[nbStrike + 1];
final double[] pvApproximation = new double[nbStrike + 1];
final double[] strike = new double[nbStrike + 1];
final double[] volExplicit = new double[nbStrike + 1];
final double[] volApprox = new double[nbStrike + 1];
final double strikeRange = 0.010;
final SwapFixedCoupon<Coupon> swap = SWAP_PAYER_DEFINITION.toDerivative(REFERENCE_DATE);
final double forward = swap.accept(PRDC, MULTICURVES);
final double pvbp = METHOD_SWAP.presentValueBasisPoint(swap, MULTICURVES);
for (int loopstrike = 0; loopstrike <= nbStrike; loopstrike++) {
strike[loopstrike] =
forward
- strikeRange
+ 3
* strikeRange
* loopstrike
/ nbStrike; // From forward-strikeRange to forward+2*strikeRange
final SwapFixedIborDefinition swapDefinition =
SwapFixedIborDefinition.from(
SETTLEMENT_DATE,
SWAP_TENOR,
EUR1YEURIBOR6M,
NOTIONAL,
strike[loopstrike],
FIXED_IS_PAYER);
final SwaptionPhysicalFixedIborDefinition swaptionDefinition =
SwaptionPhysicalFixedIborDefinition.from(EXPIRY_DATE, swapDefinition, IS_LONG);
final SwaptionPhysicalFixedIbor swaption = swaptionDefinition.toDerivative(REFERENCE_DATE);
pvExplicit[loopstrike] = METHOD_HW.presentValue(swaption, HW_MULTICURVES).getAmount(EUR);
pvApproximation[loopstrike] =
METHOD_HW_APPROXIMATION.presentValue(swaption, HW_MULTICURVES).getAmount(EUR);
final NormalFunctionData data = new NormalFunctionData(forward, pvbp, 0.01);
volExplicit[loopstrike] =
implied.getImpliedVolatility(data, swaption, pvExplicit[loopstrike]);
volApprox[loopstrike] =
implied.getImpliedVolatility(data, swaption, pvApproximation[loopstrike]);
assertEquals(
"Swaption physical - Hull-White - implied volatility - explicit/approximation",
volExplicit[loopstrike],
volApprox[loopstrike],
1.0E-3); // 0.10%
}
}
@Test(enabled = true)
/** Compare explicit formula with Monte-Carlo and long/short and payer/receiver parities. */
public void presentValueMonteCarlo() {
HullWhiteMonteCarloMethod methodMC;
methodMC =
new HullWhiteMonteCarloMethod(
new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
// Seed fixed to the DEFAULT_SEED for testing purposes.
final MultipleCurrencyAmount pvPayerLongExplicit =
METHOD_HW.presentValue(SWAPTION_LONG_PAYER, HW_MULTICURVES);
final MultipleCurrencyAmount pvPayerLongMC =
methodMC.presentValue(SWAPTION_LONG_PAYER, EUR, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - Monte Carlo",
pvPayerLongExplicit.getAmount(EUR),
pvPayerLongMC.getAmount(EUR),
1.0E+4);
final double pvMCPreviousRun = 4221400.891;
assertEquals(
"Swaption physical - Hull-White - Monte Carlo",
pvMCPreviousRun,
pvPayerLongMC.getAmount(EUR),
TOLERANCE_PV);
methodMC =
new HullWhiteMonteCarloMethod(
new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
final MultipleCurrencyAmount pvPayerShortMC =
methodMC.presentValue(SWAPTION_SHORT_PAYER, EUR, HW_MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - Monte Carlo",
-pvPayerLongMC.getAmount(EUR),
pvPayerShortMC.getAmount(EUR),
TOLERANCE_PV);
final MultipleCurrencyAmount pvReceiverLongMC =
methodMC.presentValue(SWAPTION_LONG_RECEIVER, EUR, HW_MULTICURVES);
final MultipleCurrencyAmount pvSwap = SWAP_RECEIVER.accept(PVDC, MULTICURVES);
assertEquals(
"Swaption physical - Hull-White - Monte Carlo - payer/receiver/swap parity",
pvReceiverLongMC.getAmount(EUR) + pvPayerShortMC.getAmount(EUR),
pvSwap.getAmount(EUR),
1.0E+5);
}
/**
* 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;
}