/**
* Constructor.
*
* @param cmsCap The CMS cap/floor.
* @param sabrParameter The SABR parameters.
* @param forward The forward.
* @param cutOffStrike The cut-off strike.
* @param mu The tail thickness parameter.
*/
public CMSIntegrant(
final CapFloorCMS cmsCap,
final SABRFormulaData sabrPoint,
final double forward,
final double cutOffStrike,
final double mu) {
_nbFixedPeriod = cmsCap.getUnderlyingSwap().getFixedLeg().getPayments().length;
_nbFixedPaymentYear =
(int)
Math.round(
1.0
/ cmsCap
.getUnderlyingSwap()
.getFixedLeg()
.getNthPayment(0)
.getPaymentYearFraction());
_tau = 1.0 / _nbFixedPaymentYear;
_delta = cmsCap.getPaymentTime() - cmsCap.getSettlementTime();
_eta = -_delta;
_timeToExpiry = cmsCap.getFixingTime();
_forward = forward;
_sabrExtrapolation =
new SABRExtrapolationRightFunction(forward, sabrPoint, cutOffStrike, _timeToExpiry, mu);
_isCall = cmsCap.isCap();
_strike = cmsCap.getStrike();
_factor = g(_forward) / h(_forward);
}
/** Tests the present value SABR parameters sensitivity: Method vs Calculator. */
public void presentValueSABRSensitivityMethodVsCalculator() {
final PresentValueSABRSensitivityDataBundle pvssMethod =
METHOD_EXTRAPOLATION_CAP.presentValueSABRSensitivity(CMS_CAP_LONG, SABR_MULTICURVES);
final PresentValueSABRSensitivityDataBundle pvssCalculator =
CMS_CAP_LONG.accept(PVSSSSXC, SABR_MULTICURVES);
assertEquals(
"CMS cap/floor SABR: Present value SABR sensitivity: method vs calculator",
pvssMethod,
pvssCalculator);
}
/**
* Test the present value rate sensitivity for a CMS cap with pricing by replication in the SABR
* with extrapolation framework. Method v Calculator.
*/
public void presentValueCurveSensitivityMethodVsCalculator() {
final MultipleCurrencyMulticurveSensitivity pvcsMethod =
METHOD_EXTRAPOLATION_CAP.presentValueCurveSensitivity(CMS_CAP_LONG, SABR_MULTICURVES);
final MultipleCurrencyMulticurveSensitivity pvcsCalculator =
CMS_CAP_LONG.accept(PVCSSSXC, SABR_MULTICURVES);
AssertSensitivityObjects.assertEquals(
"CMS cap/floor SABR: Present value : method vs calculator",
pvcsMethod,
pvcsCalculator,
TOLERANCE_PV_DELTA);
}
/**
* Tests the price of CMS coupon and cap/floor using replication in the SABR framework. Method v
* Calculator.
*/
public void presentValueMethodVsCalculator() {
final double pvMethod =
METHOD_EXTRAPOLATION_CAP
.presentValue(CMS_CAP_LONG, SABR_MULTICURVES)
.getAmount(EUR)
.getAmount();
final double pvCalculator =
CMS_CAP_LONG.accept(PVSSXC, SABR_MULTICURVES).getAmount(EUR).getAmount();
assertEquals(
"CMS cap/floor SABR: Present value : method vs calculator",
pvMethod,
pvCalculator,
TOLERANCE_PV);
}
@Test
/**
* Tests the price of CMS coupon and cap/floor using replication in the SABR framework. Method v
* Calculator.
*/
public void presentValueMethodVsCalculator() {
final double pvMethod =
METHOD_EXTRAPOLATION_CAP.presentValue(CMS_CAP_LONG, SABR_MULTICURVES).getAmount(EUR);
final double pvCalculator = CMS_CAP_LONG.accept(PVSSXC, SABR_MULTICURVES).getAmount(EUR);
assertEquals(
"CMS cap/floor SABR: Present value : method vs calculator",
pvMethod,
pvCalculator,
TOLERANCE_PV);
}
@Test
/**
* Test the present value rate sensitivity for a CMS cap with pricing by replication in the SABR
* with extrapolation framework. Method v Calculator.
*/
public void presentValueCurveSensitivityMethodVsCalculator() {
final MultipleCurrencyMulticurveSensitivity pvcsMethod =
METHOD_EXTRAPOLATION_CAP.presentValueCurveSensitivity(CMS_CAP_LONG, SABR_MULTICURVES);
final MultipleCurrencyMulticurveSensitivity pvcsCalculator =
CMS_CAP_LONG.accept(PVCSSSXC, SABR_MULTICURVES);
AssertSensivityObjects.assertEquals(
"CMS cap/floor SABR: Present value : method vs calculator",
pvcsMethod,
pvcsCalculator,
TOLERANCE_PV_DELTA);
}
/** Tests the cap present value SABR parameters sensitivity vs finite difference. */
public void presentValueSABRSensitivity() {
final double pv =
METHOD_EXTRAPOLATION_CAP
.presentValue(CMS_CAP_LONG, SABR_MULTICURVES)
.getAmount(EUR)
.getAmount();
final PresentValueSABRSensitivityDataBundle pvsCapLong =
METHOD_EXTRAPOLATION_CAP.presentValueSABRSensitivity(CMS_CAP_LONG, SABR_MULTICURVES);
// SABR sensitivity vs finite difference
final double shift = 0.0001;
final double shiftAlpha = 0.00001;
final double maturity =
CMS_CAP_LONG
.getUnderlyingSwap()
.getFixedLeg()
.getNthPayment(
CMS_CAP_LONG.getUnderlyingSwap().getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- CMS_CAP_LONG.getSettlementTime();
final DoublesPair expectedExpiryTenor = DoublesPair.of(CMS_CAP_LONG.getFixingTime(), maturity);
// Alpha sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterAlphaBumped =
SABRDataSets.createSABR1AlphaBumped(shiftAlpha);
final SABRSwaptionProviderDiscount sabrBundleAlphaBumped =
new SABRSwaptionProviderDiscount(MULTICURVES, sabrParameterAlphaBumped, EUR1YEURIBOR6M);
final double pvLongPayerAlphaBumped =
METHOD_EXTRAPOLATION_CAP
.presentValue(CMS_CAP_LONG, sabrBundleAlphaBumped)
.getAmount(EUR)
.getAmount();
final double expectedAlphaSensi = (pvLongPayerAlphaBumped - pv) / shiftAlpha;
assertEquals("Number of alpha sensitivity", pvsCapLong.getAlpha().getMap().keySet().size(), 1);
assertEquals(
"Alpha sensitivity expiry/tenor",
pvsCapLong.getAlpha().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Alpha sensitivity value",
expectedAlphaSensi,
pvsCapLong.getAlpha().getMap().get(expectedExpiryTenor),
TOLERANCE_PV_DELTA);
// Rho sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterRhoBumped = SABRDataSets.createSABR1RhoBumped();
final SABRSwaptionProviderDiscount sabrBundleRhoBumped =
new SABRSwaptionProviderDiscount(MULTICURVES, sabrParameterRhoBumped, EUR1YEURIBOR6M);
final double pvLongPayerRhoBumped =
METHOD_EXTRAPOLATION_CAP
.presentValue(CMS_CAP_LONG, sabrBundleRhoBumped)
.getAmount(EUR)
.getAmount();
final double expectedRhoSensi = (pvLongPayerRhoBumped - pv) / shift;
assertEquals("Number of rho sensitivity", pvsCapLong.getRho().getMap().keySet().size(), 1);
assertEquals(
"Rho sensitivity expiry/tenor",
pvsCapLong.getRho().getMap().keySet().contains(expectedExpiryTenor),
true);
assertEquals(
"Rho sensitivity value",
expectedRhoSensi,
pvsCapLong.getRho().getMap().get(expectedExpiryTenor),
TOLERANCE_PV_DELTA);
// Alpha sensitivity vs finite difference computation
final SABRInterestRateParameters sabrParameterNuBumped = SABRDataSets.createSABR1NuBumped();
final SABRSwaptionProviderDiscount sabrBundleNuBumped =
new SABRSwaptionProviderDiscount(MULTICURVES, sabrParameterNuBumped, EUR1YEURIBOR6M);
final double pvLongPayerNuBumped =
METHOD_EXTRAPOLATION_CAP
.presentValue(CMS_CAP_LONG, sabrBundleNuBumped)
.getAmount(EUR)
.getAmount();
final double expectedNuSensi = (pvLongPayerNuBumped - pv) / shift;
assertEquals("Number of nu sensitivity", pvsCapLong.getNu().getMap().keySet().size(), 1);
assertTrue(
"Nu sensitivity expiry/tenor",
pvsCapLong.getNu().getMap().keySet().contains(expectedExpiryTenor));
assertEquals(
"Nu sensitivity value",
expectedNuSensi,
pvsCapLong.getNu().getMap().get(expectedExpiryTenor),
TOLERANCE_PV_DELTA);
}
/**
* 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);
}
/**
* 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;
}