/**
* Computes the option security price curve sensitivity. The future price is computed without
* convexity adjustment.
*
* @param security The future option security.
* @param sabrData The SABR data bundle.
* @return The security price curve sensitivity.
*/
public InterestRateCurveSensitivity priceCurveSensitivity(
final InterestRateFutureOptionMarginSecurity security,
final SABRInterestRateDataBundle sabrData) {
// Forward sweep
final double priceFuture = METHOD_FUTURE.price(security.getUnderlyingFuture(), sabrData);
final double rateStrike = 1.0 - security.getStrike();
final EuropeanVanillaOption option =
new EuropeanVanillaOption(rateStrike, security.getExpirationTime(), !security.isCall());
final double forward = 1 - priceFuture;
final double delay =
security.getUnderlyingFuture().getLastTradingTime() - security.getExpirationTime();
final double[] volatilityAdjoint =
sabrData
.getSABRParameter()
.getVolatilityAdjoint(security.getExpirationTime(), delay, rateStrike, forward);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volatilityAdjoint[0]);
final double[] priceAdjoint = BLACK_FUNCTION.getPriceAdjoint(option, dataBlack);
// Backward sweep
final double priceBar = 1.0;
final double volatilityBar = priceAdjoint[2] * priceBar;
final double forwardBar = priceAdjoint[1] * priceBar + volatilityAdjoint[1] * volatilityBar;
final double priceFutureBar = -forwardBar;
final InterestRateCurveSensitivity priceFutureDerivative =
METHOD_FUTURE.priceCurveSensitivity(security.getUnderlyingFuture(), sabrData);
return priceFutureDerivative.multipliedBy(priceFutureBar);
}
/**
* Computes the present value curve sensitivity of a transaction.
*
* @param transaction The future option transaction.
* @param curves The yield curve bundle.
* @return The present value curve sensitivity.
*/
public InterestRateCurveSensitivity presentValueCurveSensitivity(
final InterestRateFutureOptionMarginTransaction transaction, final YieldCurveBundle curves) {
InterestRateCurveSensitivity securitySensitivity =
_securityMethod.priceCurveSensitivity(transaction.getUnderlyingOption(), curves);
return securitySensitivity.multipliedBy(
transaction.getQuantity()
* transaction.getUnderlyingOption().getUnderlyingFuture().getNotional()
* transaction.getUnderlyingOption().getUnderlyingFuture().getPaymentAccrualFactor());
}
/**
* Computes the present value curve sensitivity of a transaction.
*
* @param transaction The future option transaction.
* @param curves The yield curve bundle.
* @return The present value curve sensitivity.
*/
public InterestRateCurveSensitivity presentValueCurveSensitivity(
final BondFutureOptionPremiumTransaction transaction, final YieldCurveBundle curves) {
ArgumentChecker.notNull(transaction, "transaction");
ArgumentChecker.notNull(curves, "curves");
final InterestRateCurveSensitivity premiumSensitivity =
PVCSC.visit(transaction.getPremium(), curves);
final InterestRateCurveSensitivity securitySensitivity =
METHOD_SECURITY.priceCurveSensitivity(transaction.getUnderlyingOption(), curves);
return premiumSensitivity.plus(
securitySensitivity.multipliedBy(
transaction.getQuantity()
* transaction.getUnderlyingOption().getUnderlyingFuture().getNotional()));
}
@Test
/**
* Test the present value rate sensitivity against a finite difference computation; strike above
* the cut-off strike. Test sensitivity long/short parity.
*/
public void testPresentValueSensitivityAboveCutOff() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter = TestsDataSetsSABR.createSABR1();
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
InterestRateCurveSensitivity pvsCapLong =
METHOD.presentValueSensitivity(CAP_HIGH_LONG, sabrBundle);
final InterestRateCurveSensitivity pvsCapShort =
METHOD.presentValueSensitivity(CAP_HIGH_SHORT, sabrBundle);
// Long/short parity
final InterestRateCurveSensitivity pvsCapShort_1 = pvsCapShort.multipliedBy(-1);
assertEquals(pvsCapLong.getSensitivities(), pvsCapShort_1.getSensitivities());
// Present value sensitivity comparison with finite difference.
final double deltaTolerancePrice = 1.0E-1;
// Testing note: Sensitivity is for a movement of 1. 1E+2 = 1 cent for a 1 bp move.
final double deltaShift = 1.0E-7;
pvsCapLong = pvsCapLong.cleaned();
final String bumpedCurveName = "Bumped Curve";
// 1. Forward curve sensitivity
final String[] CurveNameBumpedForward = {FUNDING_CURVE_NAME, bumpedCurveName};
final CapFloorIbor capBumpedForward =
(CapFloorIbor)
CAP_HIGH_LONG_DEFINITION.toDerivative(REFERENCE_DATE, CurveNameBumpedForward);
final double[] nodeTimesForward =
new double[] {
capBumpedForward.getFixingPeriodStartTime(), capBumpedForward.getFixingPeriodEndTime()
};
final double[] sensiForwardMethod =
SensitivityFiniteDifference.curveSensitivity(
capBumpedForward,
SABR_BUNDLE,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForward,
deltaShift,
METHOD);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardMethod.length);
final List<DoublesPair> sensiPvForward = pvsCapLong.getSensitivities().get(FORWARD_CURVE_NAME);
for (int loopnode = 0; loopnode < sensiForwardMethod.length; loopnode++) {
final DoublesPair pairPv = sensiPvForward.get(loopnode);
assertEquals(
"Sensitivity cap/floor pv to forward curve: Node " + loopnode,
nodeTimesForward[loopnode],
pairPv.getFirst(),
1E-8);
// assertEquals("Sensitivity finite difference method: node sensitivity: Node " +
// loopnode, pairPv.second, sensiForwardMethod[loopnode], deltaTolerancePrice);
}
// 2. Discounting curve sensitivity
final String[] CurveNameBumpedDisc = {bumpedCurveName, FORWARD_CURVE_NAME};
final CapFloorIbor capBumpedDisc =
(CapFloorIbor) CAP_HIGH_LONG_DEFINITION.toDerivative(REFERENCE_DATE, CurveNameBumpedDisc);
final double[] nodeTimesDisc = new double[] {capBumpedDisc.getPaymentTime()};
final double[] sensiDiscMethod =
SensitivityFiniteDifference.curveSensitivity(
capBumpedDisc,
SABR_BUNDLE,
FUNDING_CURVE_NAME,
bumpedCurveName,
nodeTimesDisc,
deltaShift,
METHOD);
assertEquals("Sensitivity finite difference method: number of node", 1, sensiDiscMethod.length);
final List<DoublesPair> sensiPvDisc = pvsCapLong.getSensitivities().get(FUNDING_CURVE_NAME);
for (int loopnode = 0; loopnode < sensiDiscMethod.length; loopnode++) {
final DoublesPair pairPv = sensiPvDisc.get(loopnode);
assertEquals(
"Sensitivity cap/floor pv to forward curve: Node " + loopnode,
nodeTimesDisc[loopnode],
pairPv.getFirst(),
1E-8);
assertEquals(
"Sensitivity finite difference method: node sensitivity",
pairPv.second,
sensiDiscMethod[loopnode],
deltaTolerancePrice);
}
}
/**
* 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;
}
