SwaptionPhysicalFixedIborLMMDDMethod { public double[][] presentValueLMMSensitivity(final SwaptionPhysicalFixedIbor swaption, final LiborMarketModelDisplacedDiffusionProviderInterface lmmData) { ArgumentChecker.notNull(swaption, "Swaption"); ArgumentChecker.notNull(lmmData, "LMM provider"); final Currency ccy = swaption.getCurrency(); final MulticurveProviderInterface multicurves = lmmData.getMulticurveProvider(); final LiborMarketModelDisplacedDiffusionParameters parameters = lmmData.getLMMParameters(); final AnnuityPaymentFixed cfe = swaption.getUnderlyingSwap().accept(CFEC, multicurves); final int nbCFInit = cfe.getNumberOfPayments(); final double multFact = Math.signum(cfe.getNthPayment(0).getAmount()); final boolean isCall = (cfe.getNthPayment(0).getAmount() < 0); final double[] cftInit = new double[nbCFInit]; final double[] cfaInit = new double[nbCFInit]; for (int loopcf = 0; loopcf < nbCFInit; loopcf++) { cftInit[loopcf] = cfe.getNthPayment(loopcf).getPaymentTime(); cfaInit[loopcf] = cfe.getNthPayment(loopcf).getAmount() * -multFact; } final double timeToExpiry = swaption.getTimeToExpiry(); final int nbFactor = parameters.getNbFactor(); final double[][] volLMM = parameters.getVolatility(); final double[] timeLMM = parameters.getIborTime(); final int[] indCFDate = new int[nbCFInit]; int indStart = nbCFInit - 1; int indEnd = 0; for (int loopcf = 0; loopcf < nbCFInit; loopcf++) { indCFDate[loopcf] = Arrays.binarySearch(timeLMM, cftInit[loopcf]); if (indCFDate[loopcf] < 0) { if (timeLMM[-indCFDate[loopcf] - 1] - cftInit[loopcf] < TIME_TOLERANCE) { indCFDate[loopcf] = -indCFDate[loopcf] - 1; } else { if (cftInit[loopcf] - timeLMM[-indCFDate[loopcf] - 2] < TIME_TOLERANCE) { indCFDate[loopcf] = -indCFDate[loopcf] - 2; } else { Validate.isTrue(true, "Instrument time incompatible with LMM"); } } } if (indCFDate[loopcf] < indStart) { indStart = indCFDate[loopcf]; } if (indCFDate[loopcf] > indEnd) { indEnd = indCFDate[loopcf]; } } final int nbCF = indEnd - indStart + 1; final double[] cfa = new double[nbCF]; for (int loopcf = 0; loopcf < nbCFInit; loopcf++) { cfa[indCFDate[loopcf] - indStart] = cfaInit[loopcf]; } final double[] cft = new double[nbCF]; System.arraycopy(timeLMM, indStart, cft, 0, nbCF); final double[] dfLMM = new double[nbCF]; for (int loopcf = 0; loopcf < nbCF; loopcf++) { dfLMM[loopcf] = multicurves.getDiscountFactor(ccy, cft[loopcf]); } final double[][] gammaLMM = new double[nbCF - 1][nbFactor]; final double[] deltaLMM = new double[nbCF - 1]; System.arraycopy(parameters.getAccrualFactor(), indStart, deltaLMM, 0, nbCF - 1); final double[] aLMM = new double[nbCF - 1]; System.arraycopy(parameters.getDisplacement(), indStart, aLMM, 0, nbCF - 1); final double[] liborLMM = new double[nbCF - 1]; final double amr = parameters.getMeanReversion(); for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { gammaLMM[loopcf] = volLMM[indStart + loopcf]; liborLMM[loopcf] = (dfLMM[loopcf] / dfLMM[loopcf + 1] - 1.0d) / deltaLMM[loopcf]; } final double[] cfaMod = new double[nbCF + 1]; final double cfaMod0 = cfa[0]; cfaMod[0] = cfaMod0; cfaMod[1] = 0.0; System.arraycopy(cfa, 1, cfaMod, 2, nbCF - 1); final double[] p0 = new double[nbCF]; final double[] dP = new double[nbCF]; double b0 = 0; for (int loopcf = 0; loopcf < nbCF; loopcf++) { p0[loopcf] = dfLMM[loopcf] / dfLMM[0]; dP[loopcf] = cfaMod[loopcf + 1] * p0[loopcf]; b0 += dP[loopcf]; } final double bK = -cfaMod0; final double bM = (b0 + bK) / 2.0d; final double[] rate0Ratio = new double[nbCF - 1]; final double[][] mu0 = new double[nbCF - 1][nbFactor]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { rate0Ratio[loopcf] = (liborLMM[loopcf] + aLMM[loopcf]) / (liborLMM[loopcf] + 1 / deltaLMM[loopcf]); } for (int loopfact = 0; loopfact < nbFactor; loopfact++) { mu0[0][loopfact] = rate0Ratio[0] * gammaLMM[0][loopfact]; } for (int loopcf = 1; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { mu0[loopcf][loopfact] = mu0[loopcf - 1][loopfact] + rate0Ratio[loopcf] * gammaLMM[loopcf][loopfact]; } } final double meanReversionImpact = (Math.exp(2.0d * amr * timeToExpiry) - 1.0d) / (2.0d * amr); final double[] tau = new double[nbCF]; final double[] tau2 = new double[nbCF]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { tau2[loopcf + 1] += mu0[loopcf][loopfact] * mu0[loopcf][loopfact]; } tau2[loopcf + 1] = tau2[loopcf + 1] * meanReversionImpact; tau[loopcf + 1] = Math.sqrt(tau2[loopcf + 1]); } double sumNum = -bM; double sumDen = 0; for (int loopcf = 0; loopcf < nbCF; loopcf++) { sumNum += dP[loopcf] - dP[loopcf] * tau2[loopcf] / 2.0; sumDen += dP[loopcf] * tau[loopcf]; } final double xBar = sumNum / sumDen; final double[] pM = new double[nbCF]; for (int loopcf = 0; loopcf < nbCF; loopcf++) { pM[loopcf] = p0[loopcf] * (1 - xBar * tau[loopcf] - tau2[loopcf] / 2.0); } final double[] liborM = new double[nbCF - 1]; final double[] alphaM = new double[nbCF]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { liborM[loopcf] = (pM[loopcf] / pM[loopcf + 1] - 1.0d) / deltaLMM[loopcf]; } for (int loopcf = 0; loopcf < nbCF; loopcf++) { alphaM[loopcf] = cfaMod[loopcf + 1] * pM[loopcf] / bM; } final double[] rateMRatio = new double[nbCF - 1]; final double[][] muM = new double[nbCF - 1][nbFactor]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { rateMRatio[loopcf] = (liborM[loopcf] + aLMM[loopcf]) / (liborM[loopcf] + 1 / deltaLMM[loopcf]); } for (int loopfact = 0; loopfact < nbFactor; loopfact++) { muM[0][loopfact] = rateMRatio[0] * gammaLMM[0][loopfact]; } for (int loopcf = 1; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { muM[loopcf][loopfact] = muM[loopcf - 1][loopfact] + rateMRatio[loopcf] * gammaLMM[loopcf][loopfact]; } } double normSigmaM = 0; final double[] sigmaM = new double[nbFactor]; for (int loopfact = 0; loopfact < nbFactor; loopfact++) { for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { sigmaM[loopfact] += alphaM[loopcf + 1] * muM[loopcf][loopfact]; } normSigmaM += sigmaM[loopfact] * sigmaM[loopfact]; } final double impliedBlackVol = Math.sqrt(normSigmaM * meanReversionImpact); final EuropeanVanillaOption option = new EuropeanVanillaOption(bK, 1, isCall); final BlackPriceFunction blackFunction = new BlackPriceFunction(); final BlackFunctionData dataBlack = new BlackFunctionData(b0, 1.0, impliedBlackVol); final double[] blkAdjoint = blackFunction.getPriceAdjoint(option, dataBlack); final double pvBar = 1.0; final double impliedBlackVolBar = dfLMM[0] * blkAdjoint[2] * pvBar; final double normSigmaMBar = meanReversionImpact / (2.0 * impliedBlackVol) * impliedBlackVolBar; final double[] sigmaMBar = new double[nbFactor]; for (int loopfact = 0; loopfact < nbFactor; loopfact++) { sigmaMBar[loopfact] = 2 * sigmaM[loopfact] * normSigmaMBar; } final double[][] muMBar = new double[nbCF - 1][nbFactor]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { muMBar[loopcf][loopfact] = alphaM[loopcf + 1] * sigmaMBar[loopfact]; } } for (int loopcf = nbCF - 3; loopcf >= 0; loopcf--) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { muMBar[loopcf][loopfact] += muMBar[loopcf + 1][loopfact]; } } final double[] rateMRatioBar = new double[nbCF - 1]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { rateMRatioBar[loopcf] += gammaLMM[loopcf][loopfact] * muMBar[loopcf][loopfact]; } } final double[] alphaMBar = new double[nbCF]; for (int loopfact = 0; loopfact < nbFactor; loopfact++) { for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { alphaMBar[loopcf + 1] += muM[loopcf][loopfact] * sigmaMBar[loopfact]; } } final double[] liborMBar = new double[nbCF - 1]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { liborMBar[loopcf] = ((liborM[loopcf] + 1 / deltaLMM[loopcf]) - (liborM[loopcf] + aLMM[loopcf])) / ((liborM[loopcf] + 1 / deltaLMM[loopcf]) * (liborM[loopcf] + 1 / deltaLMM[loopcf])) * rateMRatioBar[loopcf]; } final double[] pMBar = new double[nbCF]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { pMBar[loopcf] += 1.0 / pM[loopcf + 1] / deltaLMM[loopcf] * liborMBar[loopcf]; pMBar[loopcf + 1] += -pM[loopcf] / (pM[loopcf + 1] * pM[loopcf + 1]) / deltaLMM[loopcf] * liborMBar[loopcf]; } for (int loopcf = 0; loopcf < nbCF; loopcf++) { pMBar[loopcf] += cfaMod[loopcf + 1] / bM * alphaMBar[loopcf]; } double xBarBar = 0.0; for (int loopcf = 0; loopcf < nbCF; loopcf++) { xBarBar += -p0[loopcf] * tau[loopcf] * pMBar[loopcf]; } final double sumNumBar = 1.0 / sumDen * xBarBar; final double sumDenBar = -sumNum / (sumDen * sumDen) * xBarBar; final double[] tauBar = new double[nbCF]; for (int loopcf = 0; loopcf < nbCF; loopcf++) { tauBar[loopcf] = -p0[loopcf] * xBar * pMBar[loopcf]; } for (int loopcf = 0; loopcf < nbCF; loopcf++) { tauBar[loopcf] += dP[loopcf] * sumDenBar; } final double[] tau2Bar = new double[nbCF]; for (int loopcf = 0; loopcf < nbCF; loopcf++) { tau2Bar[loopcf] = -p0[loopcf] / 2.0 * pMBar[loopcf]; } for (int loopcf = 0; loopcf < nbCF; loopcf++) { tau2Bar[loopcf] += -dP[loopcf] / 2.0 * sumNumBar; } for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { tau2Bar[loopcf + 1] += 1 / 2.0 / tau[loopcf + 1] * tauBar[loopcf + 1]; } final double[][] mu0Bar = new double[nbCF - 1][nbFactor]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { mu0Bar[loopcf][loopfact] = 2.0 * mu0[loopcf][loopfact] * meanReversionImpact * tau2Bar[loopcf + 1]; } } for (int loopcf = nbCF - 3; loopcf >= 0; loopcf--) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { mu0Bar[loopcf][loopfact] += mu0Bar[loopcf + 1][loopfact]; } } final double[][] gammaLMMBar = new double[nbCF - 1][nbFactor]; for (int loopfact = 0; loopfact < nbFactor; loopfact++) { gammaLMMBar[0][loopfact] = rateMRatio[0] * muMBar[0][loopfact]; } for (int loopcf = 1; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { gammaLMMBar[loopcf][loopfact] += rateMRatio[loopcf] * muMBar[loopcf][loopfact]; } } for (int loopfact = 0; loopfact < nbFactor; loopfact++) { gammaLMMBar[0][loopfact] += rate0Ratio[0] * mu0Bar[0][loopfact]; } for (int loopcf = 1; loopcf < nbCF - 1; loopcf++) { for (int loopfact = 0; loopfact < nbFactor; loopfact++) { gammaLMMBar[loopcf][loopfact] += rate0Ratio[loopcf] * mu0Bar[loopcf][loopfact]; } } final double[][] volLMMBar = new double[volLMM.length][nbFactor]; for (int loopcf = 0; loopcf < nbCF - 1; loopcf++) { volLMMBar[indStart + loopcf] = gammaLMMBar[loopcf]; } return volLMMBar; } private  SwaptionPhysicalFixedIborLMMDDMethod(); static SwaptionPhysicalFixedIborLMMDDMethod getInstance(); MultipleCurrencyAmount presentValue(final SwaptionPhysicalFixedIbor swaption, final LiborMarketModelDisplacedDiffusionProviderInterface lmmData); double[][] presentValueLMMSensitivity(final SwaptionPhysicalFixedIbor swaption, final LiborMarketModelDisplacedDiffusionProviderInterface lmmData); double[] presentValueDDSensitivity(final SwaptionPhysicalFixedIbor swaption, final LiborMarketModelDisplacedDiffusionProviderInterface lmmData); MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(final SwaptionPhysicalFixedIbor swaption, //CSIGNORE
      final LiborMarketModelDisplacedDiffusionProviderInterface lmmData);  }
@Test public void presentValueLMMSensitivity() { final double[][] pvLmmSensi = METHOD_LMM.presentValueLMMSensitivity(SWAPTION_PAYER_LONG, LMM_MULTICURVES); final double shift = 1.0E-6; final LiborMarketModelDisplacedDiffusionParameters parameterShiftPlus = TestsDataSetLiborMarketModelDisplacedDiffusion.createLMMParametersShiftVol(REFERENCE_DATE, SWAP_PAYER_DEFINITION.getIborLeg(), shift); final LiborMarketModelDisplacedDiffusionProviderDiscount bundleShiftPlus = new LiborMarketModelDisplacedDiffusionProviderDiscount(MULTICURVES, parameterShiftPlus, EUR); final MultipleCurrencyAmount pvShiftPlus = METHOD_LMM.presentValue(SWAPTION_PAYER_LONG, bundleShiftPlus); final LiborMarketModelDisplacedDiffusionParameters parameterShiftMinus = TestsDataSetLiborMarketModelDisplacedDiffusion.createLMMParametersShiftVol(REFERENCE_DATE, SWAP_PAYER_DEFINITION.getIborLeg(), -shift); final LiborMarketModelDisplacedDiffusionProviderDiscount bundleShiftMinus = new LiborMarketModelDisplacedDiffusionProviderDiscount(MULTICURVES, parameterShiftMinus, EUR); final MultipleCurrencyAmount pvShiftMinus = METHOD_LMM.presentValue(SWAPTION_PAYER_LONG, bundleShiftMinus); final double pvLmmSensiTotExpected = (pvShiftPlus.getAmount(EUR) - pvShiftMinus.getAmount(EUR)) / (2 * shift); double pvLmmSensiTot = 0.0; for (final double[] element : pvLmmSensi) { for (int loopfact = 0; loopfact < pvLmmSensi[0].length; loopfact++) { pvLmmSensiTot += element[loopfact]; } } assertEquals("Swaption physical - LMM - present value Lmm parameters sensitivity", pvLmmSensiTotExpected, pvLmmSensiTot, TOLERANCE_PV_DELTA); }