/**
* Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.interestrate.payments.provider;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import com.opengamma.analytics.financial.interestrate.PresentValueSABRSensitivityDataBundle;
import com.opengamma.analytics.financial.interestrate.annuity.derivative.AnnuityCouponFixed;
import com.opengamma.analytics.financial.interestrate.payments.derivative.CapFloorCMS;
import com.opengamma.analytics.financial.interestrate.payments.derivative.Payment;
import com.opengamma.analytics.financial.interestrate.swap.derivative.SwapFixedCoupon;
import com.opengamma.analytics.financial.model.option.definition.SABRInterestRateParameters;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.BlackFunctionData;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.BlackPriceFunction;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.EuropeanVanillaOption;
import com.opengamma.analytics.financial.model.volatility.smile.function.SABRFormulaData;
import com.opengamma.analytics.financial.model.volatility.smile.function.SABRHaganVolatilityFunction;
import com.opengamma.analytics.financial.model.volatility.smile.function.VolatilityFunctionProvider;
import com.opengamma.analytics.financial.provider.calculator.discounting.ParRateCurveSensitivityDiscountingCalculator;
import com.opengamma.analytics.financial.provider.calculator.discounting.ParRateDiscountingCalculator;
import com.opengamma.analytics.financial.provider.description.interestrate.SABRSwaptionProviderInterface;
import com.opengamma.analytics.financial.provider.sensitivity.multicurve.MulticurveSensitivity;
import com.opengamma.analytics.financial.provider.sensitivity.multicurve.MultipleCurrencyMulticurveSensitivity;
import com.opengamma.analytics.math.MathException;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.integration.RungeKuttaIntegrator1D;
import com.opengamma.util.ArgumentChecker;
import com.opengamma.util.money.Currency;
import com.opengamma.util.money.MultipleCurrencyAmount;
import com.opengamma.util.tuple.DoublesPair;
/**
* Class used to compute the price of a CMS cap/floor by swaption replication on a SABR formula.
* Reference: Hagan, P. S. (2003). Convexity conundrums: Pricing CMS swaps, caps, and floors. Wilmott Magazine, March, pages 38--44.
* OpenGamma implementation note: Replication pricing for linear and TEC format CMS, Version 1.2, March 2011.
*/
public class CapFloorCMSSABRReplicationMethod extends CapFloorCMSSABRReplicationAbstractMethod {
/**
* The method default instance.
*/
private static final CapFloorCMSSABRReplicationMethod INSTANCE = new CapFloorCMSSABRReplicationMethod();
/**
* Returns a default instance of the CMS cap/floor replication method. The default integration interval is 1.00 (100%).
* @return The calculation method
*/
public static CapFloorCMSSABRReplicationMethod getDefaultInstance() {
return INSTANCE;
}
/**
* The par rate calculator.
*/
private static final ParRateDiscountingCalculator PRDC = ParRateDiscountingCalculator.getInstance();
/**
* The par rate sensitivity calculator.
*/
private static final ParRateCurveSensitivityDiscountingCalculator PRCSDC = ParRateCurveSensitivityDiscountingCalculator.getInstance();
/**
* Default constructor of the CMS cap/floor replication method. The default integration interval is 1.00 (100%).
*/
private CapFloorCMSSABRReplicationMethod() {
super(1.0);
}
/**
* Constructor of the CMS cap/floor replication method with the integration range.
* @param integrationInterval Integration range.
*/
public CapFloorCMSSABRReplicationMethod(final double integrationInterval) {
super(integrationInterval);
}
/**
* Compute the present value of a CMS cap/floor by replication in SABR framework.
* For floor the replication is between 0.0 and the strike. 0.0 is used as the rates are always >=0.0 in SABR.
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle.
* @return The present value.
*/
@Override
public MultipleCurrencyAmount presentValue(final CapFloorCMS cmsCapFloor, final SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(cmsCapFloor, "CMA cap/floor");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
final Currency ccy = cmsCapFloor.getCurrency();
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRDC, sabrData.getMulticurveProvider());
final double discountFactor = sabrData.getMulticurveProvider().getDiscountFactor(ccy, cmsCapFloor.getPaymentTime());
final CMSIntegrant integrant = new CMSIntegrant(cmsCapFloor, sabrParameter, forward);
final double strike = cmsCapFloor.getStrike();
final double strikePart = discountFactor * integrant.g(forward) / integrant.h(forward) * integrant.k(strike) * integrant.bs(strike);
final double absoluteTolerance = 0.1 / (discountFactor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
// Implementation note: Each sub-integral has less than 0.1 currency unit error.
final double relativeTolerance = 1.0E-6;
final RungeKuttaIntegrator1D integrator = new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
// TODO: replace the integrator by an integrator that does not used the limits (open end). Recorded as [PLAT-1679].
// TODO: replace the integrator by an integrator that accept infinite interval (for the upper limit of cap).
double integralPart;
try {
if (cmsCapFloor.isCap()) {
integralPart = discountFactor * integrator.integrate(integrant, strike, strike + getIntegrationInterval());
} else {
integralPart = discountFactor * integrator.integrate(integrant, 0.0, strike);
}
} catch (final Exception e) {
throw new MathException(e);
}
final double priceCMS = (strikePart + integralPart) * cmsCapFloor.getNotional() * cmsCapFloor.getPaymentYearFraction();
return MultipleCurrencyAmount.of(cmsCapFloor.getCurrency(), priceCMS);
}
/**
* Computes the present value sensitivity to the yield curves of a CMS cap/floor by replication in SABR framework.
* @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
@SuppressWarnings("synthetic-access")
public MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(final CapFloorCMS cmsCapFloor, final SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(cmsCapFloor, "CMA cap/floor");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
final Currency ccy = cmsCapFloor.getCurrency();
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRDC, sabrData.getMulticurveProvider());
final double discountFactor = sabrData.getMulticurveProvider().getDiscountFactor(ccy, cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
// Common
final CMSIntegrant integrantPrice = new CMSIntegrant(cmsCapFloor, sabrParameter, forward);
final CMSDeltaIntegrant integrantDelta = new CMSDeltaIntegrant(cmsCapFloor, sabrParameter, forward);
final double factor = discountFactor / integrantDelta.h(forward) * integrantDelta.g(forward);
final double absoluteTolerance = 1.0E+1 / (factor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
final double relativeTolerance = 1.0E-2;
final RungeKuttaIntegrator1D integrator = new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
// Price
final double[] bs = integrantDelta.bsbsp(strike);
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(DoublesPair.of(cmsCapFloor.getPaymentTime(), sensiDF));
final Map<String, List<DoublesPair>> resultMapDsc = new HashMap<>();
resultMapDsc.put(sabrData.getMulticurveProvider().getName(ccy), list);
final MulticurveSensitivity dscDp = MulticurveSensitivity.ofYieldDiscounting(resultMapDsc);
final MulticurveSensitivity forwardDp = cmsCapFloor.getUnderlyingSwap().accept(PRCSDC, sabrData.getMulticurveProvider());
return MultipleCurrencyMulticurveSensitivity.of(ccy, dscDp.plus(forwardDp.multipliedBy(deltaS0)));
}
/**
* Computes the present value sensitivity to the SABR parameters of a CMS cap/floor by replication in SABR framework.
* @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 SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(cmsCapFloor, "CMA cap/floor");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
final Currency ccy = cmsCapFloor.getCurrency();
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRDC, sabrData.getMulticurveProvider());
final double discountFactor = sabrData.getMulticurveProvider().getDiscountFactor(ccy, cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity = underlyingSwap.getFixedLeg().getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1).getPaymentTime() - cmsCapFloor.getSettlementTime();
final CMSVegaIntegrant integrantVega = new CMSVegaIntegrant(cmsCapFloor, sabrParameter, forward);
final double factor = discountFactor / integrantVega.h(forward) * integrantVega.g(forward);
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 factor2 = factor * integrantVega.k(strike) * integrantVega.bs(strike);
final double[] strikePartPrice = new double[4];
final double[] volatilityAdjoint = sabrData.getSABRParameter().getVolatilityAdjoint(cmsCapFloor.getFixingTime(), maturity, strike, forward);
strikePartPrice[0] = factor2 * volatilityAdjoint[3];
strikePartPrice[1] = factor2 * volatilityAdjoint[4];
strikePartPrice[2] = factor2 * volatilityAdjoint[5];
strikePartPrice[3] = factor2 * volatilityAdjoint[6];
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] = discountFactor * integrator.integrate(integrantVega, strike, strike + getIntegrationInterval());
} else {
integralPart[loopparameter] = discountFactor * 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();
final DoublesPair expiryMaturity = DoublesPair.of(cmsCapFloor.getFixingTime(), maturity);
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 strike of a CMS cap/floor by replication in SABR framework.
* @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 SABRSwaptionProviderInterface sabrData) {
ArgumentChecker.notNull(cmsCapFloor, "CMA cap/floor");
ArgumentChecker.notNull(sabrData, "SABR swaption provider");
final Currency ccy = cmsCapFloor.getCurrency();
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRDC, sabrData.getMulticurveProvider());
final double discountFactor = sabrData.getMulticurveProvider().getDiscountFactor(ccy, cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity = underlyingSwap.getFixedLeg().getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1).getPaymentTime() - cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = DoublesPair.of(cmsCapFloor.getFixingTime(), maturity);
final CMSStrikeIntegrant integrant = new CMSStrikeIntegrant(cmsCapFloor, sabrParameter, forward);
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 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 EuropeanVanillaOption option = new EuropeanVanillaOption(strike, cmsCapFloor.getFixingTime(), cmsCapFloor.isCap());
final Function1D<SABRFormulaData, double[]> sabrFunctionAdjoint = sabrParameter.getSabrFunction().getVolatilityAdjointFunction(option, forward);
final double[] volA = sabrFunctionAdjoint.evaluate(sabrPoint);
final BlackFunctionData dataBlack = new BlackFunctionData(forward, 1.0, volA[0]);
final BlackPriceFunction blackFunction = new BlackPriceFunction();
final double[] bsA = blackFunction.getPriceAdjoint(option, dataBlack);
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) * (bsA[3] + bsA[2] * volA[2]);
return cmsCapFloor.getNotional() * cmsCapFloor.getPaymentYearFraction() * factor * (firstPart + secondPart + thirdPart);
}
/**
* Inner class to implement the integration used in price replication.
*/
private class CMSIntegrant extends Function1D<Double, Double> {
private static final double EPS = 1E-10;
private final int _nbFixedPeriod;
private final int _nbFixedPaymentYear;
private final double _tau;
private final double _delta;
private final double _eta;
private final double _timeToExpiry;
private final double _maturity;
private final double _strike;
private final double _forward;
private final double _factor;
private final SABRFormulaData _sabrData;
/**
* The function containing the SABR volatility formula.
*/
private final VolatilityFunctionProvider<SABRFormulaData> _sabrFunction;
private final BlackPriceFunction _blackFunction = new BlackPriceFunction();
private final boolean _isCall;
/**
* Constructor of the integrant.
* @param cmsCap The CMS cap/floor.
* @param sabrParameter The SABR parameters.
* @param forward The swap forward rate.
*/
public CMSIntegrant(final CapFloorCMS cmsCap, final SABRInterestRateParameters sabrParameter, final double forward) {
_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();
// TODO: A better notion of maturity may be required (using period?)
final AnnuityCouponFixed annuityFixed = cmsCap.getUnderlyingSwap().getFixedLeg();
_maturity = annuityFixed.getNthPayment(annuityFixed.getNumberOfPayments() - 1).getPaymentTime() - cmsCap.getSettlementTime();
_forward = forward;
final DoublesPair expiryMaturity = DoublesPair.of(_timeToExpiry, _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);
_sabrData = new SABRFormulaData(alpha, beta, rho, nu);
_sabrFunction = sabrParameter.getSabrFunction();
_isCall = cmsCap.isCap();
_strike = cmsCap.getStrike();
_factor = g(_forward) / h(_forward);
}
@Override
public Double evaluate(final Double x) {
final double[] kD = kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative of k.
return (kD[1] * (x - _strike) + 2.0 * kD[0]) * bs(x) * _factor;
}
/**
* The approximation of the discount factor as function of the swap rate.
* @param x The swap rate.
* @return The discount factor.
*/
double h(final double x) {
return Math.pow(1.0 + _tau * x, _eta);
}
/**
* The cash annuity.
* @param x The swap rate.
* @return The annuity.
*/
double g(final double x) {
if (x >= EPS) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
return 1.0 / x * (1.0 - nPeriodDiscount);
}
return ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
}
/**
* The factor used in the strike part and in the integration of the replication.
* @param x The swap rate.
* @return The factor.
*/
double k(final double x) {
double g;
double h;
if (x >= EPS) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
g = 1.0 / x * (1.0 - nPeriodDiscount);
h = Math.pow(1.0 + _tau * x, _eta);
} else {
g = ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
h = 1.0;
}
return h / g;
}
/**
* The first and second derivative of the function k.
* @param x The swap rate.
* @return The derivative (first element is the first derivative, second element is second derivative.
*/
double[] kpkpp(final double x) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
/**
* The value of the annuity and its first and second derivative.
*/
double g, gp, gpp;
if (x >= EPS) {
g = 1.0 / x * (1.0 - nPeriodDiscount);
gp = -g / x + _nbFixedPeriod / x / _nbFixedPaymentYear * nPeriodDiscount / periodFactor;
gpp = 2.0 / (x * x) * g - 2.0 * _nbFixedPeriod / (x * x) / _nbFixedPaymentYear * nPeriodDiscount / periodFactor - (_nbFixedPeriod + 1.0) * _nbFixedPeriod / x
/ (_nbFixedPaymentYear * _nbFixedPaymentYear) * nPeriodDiscount / (periodFactor * periodFactor);
} else {
// Implementation comment: When x is (almost) 0, useful for CMS swaps which are priced as CMS cap of strike 0.
g = ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
gp = -_nbFixedPeriod / 2.0 * (_nbFixedPeriod + 1.0) / (_nbFixedPaymentYear * _nbFixedPaymentYear);
gpp = _nbFixedPeriod / 2.0 * (_nbFixedPeriod + 1.0) * (1.0 + (_nbFixedPeriod + 2.0) / 3.0) / (_nbFixedPaymentYear * _nbFixedPaymentYear * _nbFixedPaymentYear);
}
final double g2 = g * g;
final double h = Math.pow(1.0 + _tau * x, _eta);
final double hp = _eta * _tau * h / periodFactor;
final double hpp = (_eta - 1.0) * _tau * hp / periodFactor;
final double kp = hp / g - h * gp / g2;
final double kpp = hpp / g - 2 * hp * gp / g2 - h * (gpp / g2 - 2 * (gp * gp) / (g2 * g));
return new double[] {kp, kpp};
}
/**
* The Black-Scholes formula with numeraire 1 as function of the strike.
* @param strike The strike.
* @return The Black-Scholes formula.
*/
double bs(final double strike) {
final EuropeanVanillaOption option = new EuropeanVanillaOption(strike, _timeToExpiry, _isCall);
final Function1D<SABRFormulaData, Double> funcSabr = _sabrFunction.getVolatilityFunction(option, _forward);
final double volatility = funcSabr.evaluate(_sabrData);
final BlackFunctionData dataBlack = new BlackFunctionData(_forward, 1.0, volatility);
final Function1D<BlackFunctionData, Double> func = _blackFunction.getPriceFunction(option);
return func.evaluate(dataBlack);
}
/**
* Gets the eps field.
* @return the eps
*/
public double getEps() {
return EPS;
}
}
private class CMSDeltaIntegrant extends CMSIntegrant {
private final double[] _nnp;
/**
* @param cmsCap
* @param sabrParameter
* @param forward
*/
public CMSDeltaIntegrant(final CapFloorCMS cmsCap, final SABRInterestRateParameters sabrParameter, final double forward) {
super(cmsCap, sabrParameter, forward);
_nnp = nnp(forward);
}
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double x) {
final double[] kD = super.kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative of k.
final double[] bs = bsbsp(x);
return (kD[1] * (x - super._strike) + 2.0 * kD[0]) * (_nnp[1] * bs[0] + _nnp[0] * bs[1]);
}
private double[] nnp(final double x) {
final double[] result = new double[2];
final double[] ggp = ggp(x);
final double[] hhp = hhp(x);
result[0] = ggp[0] / hhp[0];
result[1] = ggp[1] / hhp[0] - ggp[0] * hhp[1] / (hhp[0] * hhp[0]);
return result;
}
@SuppressWarnings("synthetic-access")
private double[] ggp(final double x) {
final double[] result = new double[2];
if (x >= getEps()) {
final double periodFactor = 1 + x / super._nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -super._nbFixedPeriod);
result[0] = 1.0 / x * (1.0 - nPeriodDiscount);
result[1] = -result[0] / x + super._tau * super._nbFixedPeriod / x * nPeriodDiscount / periodFactor;
} else {
result[0] = super._nbFixedPeriod * super._tau;
result[1] = -super._nbFixedPeriod * (super._nbFixedPeriod + 1.0) * super._tau * super._tau / 2.0;
}
return result;
}
@SuppressWarnings("synthetic-access")
private double[] hhp(final double x) {
final double[] result = new double[2];
result[0] = Math.pow(1.0 + super._tau * x, super._eta);
result[1] = super._eta * super._tau * result[0] / (1 + x * super._tau);
return result;
}
/**
* The Black-Scholes formula and its derivative with respect to the forward.
* @param strike The strike.
* @return The Black-Scholes formula and its derivative.
*/
@SuppressWarnings("synthetic-access")
double[] bsbsp(final double strike) {
final double[] result = new double[2];
final EuropeanVanillaOption option = new EuropeanVanillaOption(strike, super._timeToExpiry, super._isCall);
final SABRHaganVolatilityFunction sabrHaganFunction = (SABRHaganVolatilityFunction) super._sabrFunction;
final double[] volatility = sabrHaganFunction.getVolatilityAdjoint(option, super._forward, super._sabrData);
final BlackFunctionData dataBlack = new BlackFunctionData(super._forward, 1.0, volatility[0]);
final double[] bsAdjoint = super._blackFunction.getPriceAdjoint(option, dataBlack);
result[0] = bsAdjoint[0];
result[1] = bsAdjoint[1] + bsAdjoint[2] * volatility[1];
return result;
}
}
private class CMSVegaIntegrant extends CMSIntegrant {
private int _parameterIndex;
/**
* @param cmsCap
* @param sabrParameter
* @param forward
*/
public CMSVegaIntegrant(final CapFloorCMS cmsCap, final SABRInterestRateParameters sabrParameter, final double forward) {
super(cmsCap, sabrParameter, forward);
}
/**
* Sets the _parameterIndex field.
* @param _parameterIndex the _parameterIndex
*/
public void setParameterIndex(final int parameterIndex) {
this._parameterIndex = parameterIndex;
}
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double x) {
final double[] kD = super.kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative of k.
final EuropeanVanillaOption option = new EuropeanVanillaOption(x, super._timeToExpiry, super._isCall);
final SABRHaganVolatilityFunction sabrHaganFunction = (SABRHaganVolatilityFunction) super._sabrFunction;
final double[] volatilityAdjoint = sabrHaganFunction.getVolatilityAdjoint(option, super._forward, super._sabrData);
return super._factor * (kD[1] * (x - super._strike) + 2.0 * kD[0]) * bs(x) * volatilityAdjoint[3 + _parameterIndex];
}
/**
* The derivative with respect to the volatility of the Black-Scholes formula with numeraire 1.
* @param strike The strike.
* @return The Black-Scholes formula derivative with respect to volatility.
*/
@SuppressWarnings("synthetic-access")
@Override
double bs(final double strike) {
final EuropeanVanillaOption option = new EuropeanVanillaOption(strike, super._timeToExpiry, super._isCall);
final Function1D<SABRFormulaData, Double> funcSabr = super._sabrFunction.getVolatilityFunction(option, super._forward);
final double volatility = funcSabr.evaluate(super._sabrData);
final BlackFunctionData dataBlack = new BlackFunctionData(super._forward, 1.0, volatility);
final double[] bsAdjoint = super._blackFunction.getPriceAdjoint(option, dataBlack);
return bsAdjoint[2];
}
}
private class CMSStrikeIntegrant extends CMSIntegrant {
/**
* @param cmsCap
* @param sabrParameter
* @param forward
*/
public CMSStrikeIntegrant(final CapFloorCMS cmsCap, final SABRInterestRateParameters sabrParameter, final double forward) {
super(cmsCap, sabrParameter, forward);
}
@Override
public Double evaluate(final Double x) {
final double[] kD = super.kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative of k.
return -kD[1] * bs(x);
}
} // End CMSStrikeIntegrant
}