public MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(final SwaptionCashFixedIbor swaption, final HullWhiteOneFactorProviderInterface hullWhite) {
ArgumentChecker.notNull(swaption, "Swaption");
ArgumentChecker.notNull(hullWhite, "Hull-White provider");
final Currency ccy = swaption.getCurrency();
final HullWhiteOneFactorPiecewiseConstantParameters parameters = hullWhite.getHullWhiteParameters();
final MulticurveProviderInterface multicurves = hullWhite.getMulticurveProvider();
// Forward sweep
final double expiryTime = swaption.getTimeToExpiry();
final int nbFixed = swaption.getUnderlyingSwap().getFixedLeg().getNumberOfPayments();
final double[] alphaFixed = new double[nbFixed];
final double[] dfFixed = new double[nbFixed];
final double[] discountedCashFlowFixed = new double[nbFixed];
final double[] testdiscountedCashFlowFixed = new double[nbFixed];
for (int loopcf = 0; loopcf < nbFixed; loopcf++) {
alphaFixed[loopcf] = MODEL.alpha(parameters, 0.0, expiryTime, expiryTime, swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf).getPaymentTime());
dfFixed[loopcf] = multicurves.getDiscountFactor(ccy, swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf).getPaymentTime());
discountedCashFlowFixed[loopcf] = dfFixed[loopcf] * swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf).getPaymentYearFraction()
* swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf).getNotional();
testdiscountedCashFlowFixed[loopcf] = discountedCashFlowFixed[loopcf];
}
testdiscountedCashFlowFixed[0] += 1.0;
final AnnuityPaymentFixed cfeIbor = swaption.getUnderlyingSwap().getSecondLeg().accept(CFEC, multicurves);
final double[] alphaIbor = new double[cfeIbor.getNumberOfPayments()];
final double[] dfIbor = new double[cfeIbor.getNumberOfPayments()];
final double[] discountedCashFlowIbor = new double[cfeIbor.getNumberOfPayments()];
for (int loopcf = 0; loopcf < cfeIbor.getNumberOfPayments(); loopcf++) {
alphaIbor[loopcf] = MODEL.alpha(parameters, 0.0, expiryTime, expiryTime, cfeIbor.getNthPayment(loopcf).getPaymentTime());
dfIbor[loopcf] = multicurves.getDiscountFactor(ccy, cfeIbor.getNthPayment(loopcf).getPaymentTime());
discountedCashFlowIbor[loopcf] = dfIbor[loopcf] * cfeIbor.getNthPayment(loopcf).getAmount();
}
final AnnuityPaymentFixed cfe = swaption.getUnderlyingSwap().accept(CFEC, multicurves);
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(parameters, 0.0, expiryTime, expiryTime, cfe.getNthPayment(loopcf).getPaymentTime());
df[loopcf] = multicurves.getDiscountFactor(ccy, cfe.getNthPayment(loopcf).getPaymentTime());
discountedCashFlow[loopcf] = df[loopcf] * cfe.getNthPayment(loopcf).getAmount();
}
final double kappa = MODEL.kappa(discountedCashFlow, alpha);
final int nbFixedPaymentYear = (int) Math.round(1.0 / swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(0).getPaymentYearFraction());
final double[] derivativesRate = new double[3];
final double[] derivativesAnnuity = new double[3];
final double x0 = 0.0; // (swaption.getUnderlyingSwap().getFixedLeg().isPayer()) ? Math.max(kappa, 0) : Math.min(kappa, 0);
final double rate = swapRate(x0, discountedCashFlowFixed, alphaFixed, discountedCashFlowIbor, alphaIbor, derivativesRate);
final double annuity = annuityCash(rate, nbFixedPaymentYear, swaption.getUnderlyingSwap().getFixedLeg().getNumberOfPayments(), derivativesAnnuity);
final double[] u = new double[4];
u[0] = annuity * (swaption.getStrike() - rate);
u[1] = (swaption.getStrike() - rate) * derivativesAnnuity[0] * derivativesRate[0] - derivativesRate[0] * annuity;
u[2] = (swaption.getStrike() - rate) * (derivativesAnnuity[0] * derivativesRate[1] + derivativesAnnuity[1] * derivativesRate[0] * derivativesRate[0]) - 2 * derivativesAnnuity[0]
* derivativesRate[0] * derivativesRate[0] - annuity * derivativesRate[1];
u[3] = (-3 * derivativesRate[0] * (derivativesAnnuity[0] * derivativesRate[1] + derivativesAnnuity[1] * derivativesRate[0] * derivativesRate[0]))
- (2 * derivativesAnnuity[0] * derivativesRate[0] * derivativesRate[1])
+ ((swaption.getStrike() - rate) * (derivativesAnnuity[0] * derivativesRate[2] + 3 * derivativesAnnuity[1] * derivativesRate[0] * derivativesRate[1] + derivativesAnnuity[2]
* derivativesRate[0] * derivativesRate[0] * derivativesRate[0])) - (rate * derivativesRate[2]);
final double kappatilde = kappa + alphaIbor[0];
final double alpha0tilde = alphaIbor[0] + x0;
double ncdf;
final double npdf = NORMAL.getPDF(kappatilde);
double pv;
if (!swaption.getUnderlyingSwap().getFixedLeg().isPayer()) {
ncdf = NORMAL.getCDF(kappatilde);
pv = (u[0] - u[1] * alpha0tilde + u[2] * (1 + alpha[0] * alpha[0]) / 2.0 - u[3] * (alpha0tilde * alpha0tilde * alpha0tilde + 3.0 * alpha0tilde) / 6.0) * ncdf
+ (-u[1] - u[2] * (-2.0 * alpha0tilde + kappatilde) / 2.0 + u[3] * (-3 * alpha0tilde * alpha0tilde + 3.0 * kappatilde * alpha0tilde - kappatilde * kappatilde - 2.0) / 6.0) * npdf;
} else {
ncdf = NORMAL.getCDF(-kappatilde);
pv = -(u[0] - u[1] * alpha0tilde + u[2] * (1 + alpha[0] * alpha[0]) / 2.0 - u[3] * (alpha0tilde * alpha0tilde * alpha0tilde + 3.0 * alpha0tilde) / 6.0) * ncdf
+ (-u[1] - u[2] * (-2.0 * alpha0tilde + kappatilde) / 2.0 + u[3] * (-3 * alpha0tilde * alpha0tilde + 3.0 * kappatilde * alpha0tilde - kappatilde * kappatilde - 2.0) / 6.0) * npdf;
}
final double notional = Math.abs(swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(0).getNotional());
// Backward sweep
final double pvTotalBar = 1.0;
final double pvBar = notional * dfIbor[0] * (swaption.isLong() ? 1.0 : -1.0) * pvTotalBar;
final double[] uBar = new double[4];
if (!swaption.getUnderlyingSwap().getFixedLeg().isPayer()) {
uBar[0] = ncdf * pvBar;
uBar[1] = (-alpha0tilde * ncdf - npdf) * pvBar;
uBar[2] = ((1 + alpha[0] * alpha[0]) / 2.0 * ncdf - (-2.0 * alpha0tilde + kappatilde) / 2.0 * npdf) * pvBar;
uBar[3] = (-(alpha0tilde * alpha0tilde * alpha0tilde + 3.0 * alpha0tilde) / 6.0 * ncdf + (-3 * alpha0tilde * alpha0tilde + 3.0 * kappatilde * alpha0tilde - kappatilde * kappatilde - 2.0) / 6.0
* npdf)
* pvBar;
} else {
uBar[0] = -ncdf * pvBar;
uBar[1] = (+alpha0tilde * ncdf - npdf) * pvBar;
uBar[2] = (-(1 + alpha[0] * alpha[0]) / 2.0 * ncdf - (-2.0 * alpha0tilde + kappatilde) / 2.0 * npdf) * pvBar;
uBar[3] = ((alpha0tilde * alpha0tilde * alpha0tilde + 3.0 * alpha0tilde) / 6.0 * ncdf + (-3 * alpha0tilde * alpha0tilde + 3.0 * kappatilde * alpha0tilde - kappatilde * kappatilde - 2.0) / 6.0
* npdf)
* pvBar;
}
final double annuityBar = (swaption.getStrike() - rate) * uBar[0] - derivativesRate[0] * uBar[1] + -derivativesRate[1] * uBar[2];
final double[] derivativesAnnuityBar = new double[3];
derivativesAnnuityBar[0] = (swaption.getStrike() - rate) * derivativesRate[0] * uBar[1] + ((swaption.getStrike() - rate) * derivativesRate[1] - 2.0 * derivativesRate[0] * derivativesRate[0])
* uBar[2] + (-3 * derivativesRate[0] * derivativesRate[1] - 2 * derivativesRate[0] * derivativesRate[1] + (swaption.getStrike() - rate) * derivativesRate[2]) * uBar[3];
derivativesAnnuityBar[1] = (swaption.getStrike() - rate) * derivativesRate[0] * derivativesRate[0] * uBar[2]
+ (-3 * derivativesRate[0] * derivativesRate[0] * derivativesRate[0] + (swaption.getStrike() - rate) * 3 * derivativesRate[0] * derivativesRate[1]) * uBar[3];
derivativesAnnuityBar[2] = (swaption.getStrike() - rate) * derivativesRate[0] * derivativesRate[0] * derivativesRate[0] * uBar[3];
final double rateBar = (derivativesAnnuity[1] * derivativesAnnuityBar[0])
+ (derivativesAnnuity[2] * derivativesAnnuityBar[1])
+ (derivativesAnnuity[0] * annuityBar)
- (annuity * uBar[0])
- (derivativesAnnuity[0] * derivativesRate[0] * uBar[1])
- ((derivativesAnnuity[0] * derivativesRate[1] + derivativesAnnuity[1] * derivativesRate[0] * derivativesRate[0]) * uBar[2])
- (((derivativesAnnuity[0] * derivativesRate[2] + 3 * derivativesAnnuity[1] * derivativesRate[0] * derivativesRate[1] + derivativesAnnuity[2] * derivativesRate[0] * derivativesRate[0]
* derivativesRate[0]) + derivativesRate[2]) * uBar[3]);
final double[] derivativesRateBar = new double[3];
derivativesRateBar[0] = ((swaption.getStrike() - rate) * derivativesAnnuity[0] - annuity)
* uBar[1]
+ ((swaption.getStrike() - rate) * (2.0 * derivativesAnnuity[1] * derivativesRate[0]) - 4 * derivativesAnnuity[0] * derivativesRate[0])
* uBar[2]
+ (-3 * (derivativesAnnuity[0] * derivativesRate[1] + 3.0 * derivativesAnnuity[1] * derivativesRate[0] * derivativesRate[0]) - 2 * derivativesAnnuity[0] * derivativesRate[1] + (swaption
.getStrike() - rate) * (3 * derivativesAnnuity[1] * derivativesRate[1] + derivativesAnnuity[2] * 3.0 * derivativesRate[0] * derivativesRate[0])) * uBar[3];
derivativesRateBar[1] = ((swaption.getStrike() - rate) * (derivativesAnnuity[0]) - annuity) * uBar[2]
+ (-3 * derivativesRate[0] * (derivativesAnnuity[0]) - 2 * derivativesAnnuity[0] * derivativesRate[0] + (swaption.getStrike() - rate) * (3 * derivativesAnnuity[1] * derivativesRate[0]))
* uBar[3];
derivativesRateBar[2] = ((swaption.getStrike() - rate) * derivativesAnnuity[0] - rate) * uBar[3];
// double kappaBar = 0.0;
final double[] discountedCashFlowFixedBar = new double[nbFixed];
final double[] discountedCashFlowIborBar = new double[cfeIbor.getNumberOfPayments()];
swapRateAdjointDiscountedCF(x0, discountedCashFlowFixed, alphaFixed, discountedCashFlowIbor, alphaIbor, rateBar, derivativesRateBar, derivativesRate, discountedCashFlowFixedBar,
discountedCashFlowIborBar);
final double[] dfFixedBar = new double[nbFixed];
final List<DoublesPair> listDf = new ArrayList<>();
for (int loopcf = 0; loopcf < nbFixed; loopcf++) {
dfFixedBar[loopcf] = swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf).getPaymentYearFraction() * swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf).getNotional()
* discountedCashFlowFixedBar[loopcf];
final DoublesPair dfSensi = new DoublesPair(swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf).getPaymentTime(), -swaption.getUnderlyingSwap().getFixedLeg().getNthPayment(loopcf)
.getPaymentTime()
* dfFixed[loopcf] * dfFixedBar[loopcf]);
listDf.add(dfSensi);
}
final double[] dfIborBar = new double[cfeIbor.getNumberOfPayments()];
final double[] cfeAmountIborBar = new double[cfeIbor.getNumberOfPayments()];
dfIborBar[0] = pv * notional * (swaption.isLong() ? 1.0 : -1.0);
for (int loopcf = 0; loopcf < cfe.getNumberOfPayments(); loopcf++) {
dfIborBar[loopcf] += cfeIbor.getNthPayment(loopcf).getAmount() * discountedCashFlowIborBar[loopcf];
final DoublesPair dfSensi = new DoublesPair(cfeIbor.getNthPayment(loopcf).getPaymentTime(), -cfeIbor.getNthPayment(loopcf).getPaymentTime() * dfIbor[loopcf] * dfIborBar[loopcf]);
listDf.add(dfSensi);
cfeAmountIborBar[loopcf] = dfIbor[loopcf] * discountedCashFlowIborBar[loopcf];
}
final Map<String, List<DoublesPair>> pvsDF = new HashMap<>();
pvsDF.put(multicurves.getName(ccy), listDf);
MulticurveSensitivity sensitivity = MulticurveSensitivity.ofYieldDiscounting(pvsDF);
final Map<Double, MulticurveSensitivity> cfeIborCurveSensi = swaption.getUnderlyingSwap().getSecondLeg().accept(CFECSC, multicurves);
for (int loopcf = 0; loopcf < cfeIbor.getNumberOfPayments(); loopcf++) {
final MulticurveSensitivity sensiCfe = cfeIborCurveSensi.get(cfeIbor.getNthPayment(loopcf).getPaymentTime());
if (!(sensiCfe == null)) { // There is some sensitivity to that cfe.