//------------------------------------------------------------------------- /// <summary> /// Calculates the present value sensitivity to the SABR model parameters of the swaption product. /// <para> /// The sensitivity of the present value to the SABR model parameters, alpha, beta, rho and nu. /// /// </para> /// </summary> /// <param name="swaption"> the swaption product </param> /// <param name="ratesProvider"> the rates provider </param> /// <param name="swaptionVolatilities"> the volatilities </param> /// <returns> the point sensitivity to the SABR model parameters </returns> public virtual PointSensitivityBuilder presentValueSensitivityModelParamsSabr(ResolvedSwaption swaption, RatesProvider ratesProvider, SabrSwaptionVolatilities swaptionVolatilities) { validate(swaption, ratesProvider, swaptionVolatilities); double expiry = swaptionVolatilities.relativeTime(swaption.Expiry); ResolvedSwap underlying = swaption.Underlying; ResolvedSwapLeg fixedLeg = this.fixedLeg(underlying); double tenor = swaptionVolatilities.tenor(fixedLeg.StartDate, fixedLeg.EndDate); double shift = swaptionVolatilities.shift(expiry, tenor); double pvbp = SwapPricer.LegPricer.pvbp(fixedLeg, ratesProvider); double strike = SwapPricer.LegPricer.couponEquivalent(fixedLeg, ratesProvider, pvbp); if (expiry < 0d) { // Option has expired already return(PointSensitivityBuilder.none()); } double forward = SwapPricer.parRate(underlying, ratesProvider); double volatility = swaptionVolatilities.volatility(expiry, tenor, strike, forward); DoubleArray derivative = swaptionVolatilities.volatilityAdjoint(expiry, tenor, strike, forward).Derivatives; // Backward sweep double vega = Math.Abs(pvbp) * BlackFormulaRepository.vega(forward + shift, strike + shift, expiry, volatility) * swaption.LongShort.sign(); // sensitivities Currency ccy = fixedLeg.Currency; SwaptionVolatilitiesName name = swaptionVolatilities.Name; return(PointSensitivityBuilder.of(SwaptionSabrSensitivity.of(name, expiry, tenor, ALPHA, ccy, vega * derivative.get(2)), SwaptionSabrSensitivity.of(name, expiry, tenor, BETA, ccy, vega * derivative.get(3)), SwaptionSabrSensitivity.of(name, expiry, tenor, RHO, ccy, vega * derivative.get(4)), SwaptionSabrSensitivity.of(name, expiry, tenor, NU, ccy, vega * derivative.get(5)))); }
//------------------------------------------------------------------------- /// <summary> /// Calculates the present value sensitivity of the swaption product to the rate curves. /// <para> /// The present value sensitivity is computed in a "sticky model parameter" style, i.e. the sensitivity to the /// curve nodes with the SABR model parameters unchanged. This sensitivity does not include a potential /// re-calibration of the model parameters to the raw market data. /// /// </para> /// </summary> /// <param name="swaption"> the swaption product </param> /// <param name="ratesProvider"> the rates provider </param> /// <param name="swaptionVolatilities"> the volatilities </param> /// <returns> the point sensitivity to the rate curves </returns> public virtual PointSensitivityBuilder presentValueSensitivityRatesStickyModel(ResolvedSwaption swaption, RatesProvider ratesProvider, SabrSwaptionVolatilities swaptionVolatilities) { validate(swaption, ratesProvider, swaptionVolatilities); ZonedDateTime expiryDateTime = swaption.Expiry; double expiry = swaptionVolatilities.relativeTime(expiryDateTime); ResolvedSwap underlying = swaption.Underlying; ResolvedSwapLeg fixedLeg = this.fixedLeg(underlying); if (expiry < 0d) { // Option has expired already return(PointSensitivityBuilder.none()); } double forward = SwapPricer.parRate(underlying, ratesProvider); double pvbp = SwapPricer.LegPricer.pvbp(fixedLeg, ratesProvider); double strike = SwapPricer.LegPricer.couponEquivalent(fixedLeg, ratesProvider, pvbp); double tenor = swaptionVolatilities.tenor(fixedLeg.StartDate, fixedLeg.EndDate); double shift = swaptionVolatilities.shift(expiry, tenor); ValueDerivatives volatilityAdj = swaptionVolatilities.volatilityAdjoint(expiry, tenor, strike, forward); bool isCall = fixedLeg.PayReceive.Pay; // Payer at strike is exercise when rate > strike, i.e. call on rate // Backward sweep PointSensitivityBuilder pvbpDr = SwapPricer.LegPricer.pvbpSensitivity(fixedLeg, ratesProvider); PointSensitivityBuilder forwardDr = SwapPricer.parRateSensitivity(underlying, ratesProvider); double shiftedForward = forward + shift; double shiftedStrike = strike + shift; double price = BlackFormulaRepository.price(shiftedForward, shiftedStrike, expiry, volatilityAdj.Value, isCall); double delta = BlackFormulaRepository.delta(shiftedForward, shiftedStrike, expiry, volatilityAdj.Value, isCall); double vega = BlackFormulaRepository.vega(shiftedForward, shiftedStrike, expiry, volatilityAdj.Value); double sign = swaption.LongShort.sign(); return(pvbpDr.multipliedBy(price * sign * Math.Sign(pvbp)).combinedWith(forwardDr.multipliedBy((delta + vega * volatilityAdj.getDerivative(0)) * Math.Abs(pvbp) * sign))); }
//------------------------------------------------------------------------- /// <summary> /// Calculates the present value sensitivity of the swaption product to the rate curves. /// <para> /// The present value sensitivity is computed in a "sticky model parameter" style, i.e. the sensitivity to the /// curve nodes with the SABR model parameters unchanged. This sensitivity does not include a potential /// re-calibration of the model parameters to the raw market data. /// /// </para> /// </summary> /// <param name="swaption"> the swaption product </param> /// <param name="ratesProvider"> the rates provider </param> /// <param name="swaptionVolatilities"> the volatilities </param> /// <returns> the point sensitivity to the rate curves </returns> public virtual PointSensitivityBuilder presentValueSensitivityRatesStickyModel(ResolvedSwaption swaption, RatesProvider ratesProvider, SabrSwaptionVolatilities swaptionVolatilities) { validate(swaption, ratesProvider, swaptionVolatilities); ZonedDateTime expiryDateTime = swaption.Expiry; double expiry = swaptionVolatilities.relativeTime(expiryDateTime); ResolvedSwap underlying = swaption.Underlying; ResolvedSwapLeg fixedLeg = this.fixedLeg(underlying); if (expiry < 0d) { // Option has expired already return(PointSensitivityBuilder.none()); } double forward = SwapPricer.parRate(underlying, ratesProvider); ValueDerivatives annuityDerivative = SwapPricer.LegPricer.annuityCashDerivative(fixedLeg, forward); double annuityCash = annuityDerivative.Value; double annuityCashDr = annuityDerivative.getDerivative(0); LocalDate settlementDate = ((CashSwaptionSettlement)swaption.SwaptionSettlement).SettlementDate; double discountSettle = ratesProvider.discountFactor(fixedLeg.Currency, settlementDate); double strike = calculateStrike(fixedLeg); double tenor = swaptionVolatilities.tenor(fixedLeg.StartDate, fixedLeg.EndDate); double shift = swaptionVolatilities.shift(expiry, tenor); ValueDerivatives volatilityAdj = swaptionVolatilities.volatilityAdjoint(expiry, tenor, strike, forward); bool isCall = fixedLeg.PayReceive.Pay; double shiftedForward = forward + shift; double shiftedStrike = strike + shift; double price = BlackFormulaRepository.price(shiftedForward, shiftedStrike, expiry, volatilityAdj.Value, isCall); double delta = BlackFormulaRepository.delta(shiftedForward, shiftedStrike, expiry, volatilityAdj.Value, isCall); double vega = BlackFormulaRepository.vega(shiftedForward, shiftedStrike, expiry, volatilityAdj.Value); PointSensitivityBuilder forwardSensi = SwapPricer.parRateSensitivity(underlying, ratesProvider); PointSensitivityBuilder discountSettleSensi = ratesProvider.discountFactors(fixedLeg.Currency).zeroRatePointSensitivity(settlementDate); double sign = swaption.LongShort.sign(); return(forwardSensi.multipliedBy(sign * discountSettle * (annuityCash * (delta + vega * volatilityAdj.getDerivative(0)) + annuityCashDr * price)).combinedWith(discountSettleSensi.multipliedBy(sign * annuityCash * price))); }