//-------------------------------------------------------------------------
/// <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)));
}
//-------------------------------------------------------------------------
/// <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 strike = calculateStrike(fixedLeg);
if (expiry < 0d)
{ // Option has expired already
return(PointSensitivityBuilder.none());
}
double forward = SwapPricer.parRate(underlying, ratesProvider);
double volatility = swaptionVolatilities.volatility(expiry, tenor, strike, forward);
double numeraire = calculateNumeraire(swaption, fixedLeg, forward, ratesProvider);
DoubleArray derivative = swaptionVolatilities.volatilityAdjoint(expiry, tenor, strike, forward).Derivatives;
double vega = numeraire * swaption.LongShort.sign() * BlackFormulaRepository.vega(forward + shift, strike + shift, expiry, volatility);
// 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 price sensitivity to the Black volatility used for the pricing of the bond future option
/// based on the price of the underlying future.
/// </summary>
/// <param name="futureOption"> the option product </param>
/// <param name="discountingProvider"> the discounting provider </param>
/// <param name="volatilities"> the volatilities </param>
/// <param name="futurePrice"> the underlying future price </param>
/// <returns> the sensitivity </returns>
public BondFutureOptionSensitivity priceSensitivityModelParamsVolatility(ResolvedBondFutureOption futureOption, LegalEntityDiscountingProvider discountingProvider, BlackBondFutureVolatilities volatilities, double futurePrice)
{
ArgChecker.isTrue(futureOption.PremiumStyle.Equals(FutureOptionPremiumStyle.DAILY_MARGIN), "Premium style should be DAILY_MARGIN");
double strike = futureOption.StrikePrice;
ResolvedBondFuture future = futureOption.UnderlyingFuture;
double volatility = volatilities.volatility(futureOption.Expiry, future.LastTradeDate, strike, futurePrice);
double timeToExpiry = volatilities.relativeTime(futureOption.Expiry);
double vega = BlackFormulaRepository.vega(futurePrice, strike, timeToExpiry, volatility);
return(BondFutureOptionSensitivity.of(volatilities.Name, timeToExpiry, future.LastTradeDate, strike, futurePrice, future.Currency, vega));
}
//-------------------------------------------------------------------------
private double[] weights(double forward, double strike, double[] strikes, double timeToExpiry, double atmVol)
{
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] mat = new double[3][3];
double[][] mat = RectangularArrays.ReturnRectangularDoubleArray(3, 3);
double[] vec = new double[3];
for (int i = 0; i < 3; ++i)
{
mat[0][i] = BlackFormulaRepository.vega(forward, strikes[i], timeToExpiry, atmVol);
mat[1][i] = BlackFormulaRepository.vanna(forward, strikes[i], timeToExpiry, atmVol);
mat[2][i] = BlackFormulaRepository.volga(forward, strikes[i], timeToExpiry, atmVol);
}
vec[0] = BlackFormulaRepository.vega(forward, strike, timeToExpiry, atmVol);
vec[1] = BlackFormulaRepository.vanna(forward, strike, timeToExpiry, atmVol);
vec[2] = BlackFormulaRepository.volga(forward, strike, timeToExpiry, atmVol);
DecompositionResult res = SVD.apply(DoubleMatrix.ofUnsafe(mat));
return(res.solve(vec));
}
//-------------------------------------------------------------------------
public virtual void test_vega_presentValueVega()
{
double vegaCall = PRICER.vega(CALL_OTM, RATES_PROVIDER, VOLS);
CurrencyAmount pvVegaCall = PRICER.presentValueVega(CALL_OTM, RATES_PROVIDER, VOLS);
double vegaPut = PRICER.vega(PUT_ITM, RATES_PROVIDER, VOLS);
CurrencyAmount pvVegaPut = PRICER.presentValueVega(PUT_ITM, RATES_PROVIDER, VOLS);
double timeToExpiry = VOLS.relativeTime(EXPIRY);
double dfDom = RATES_PROVIDER.discountFactor(USD, PAYMENT_DATE);
double forward = PRICER.DiscountingFxSingleProductPricer.forwardFxRate(FX_PRODUCT_HIGH, RATES_PROVIDER).fxRate(CURRENCY_PAIR);
double vol = SMILE_TERM.volatility(timeToExpiry, STRIKE_RATE_HIGH, forward);
double expectedVega = dfDom * BlackFormulaRepository.vega(forward, STRIKE_RATE_HIGH, timeToExpiry, vol);
double expectedPvVega = -NOTIONAL *dfDom *BlackFormulaRepository.vega(forward, STRIKE_RATE_HIGH, timeToExpiry, vol);
assertEquals(vegaCall, expectedVega, TOL);
assertEquals(pvVegaCall.Currency, USD);
assertEquals(pvVegaCall.Amount, expectedPvVega, NOTIONAL * TOL);
assertEquals(vegaPut, expectedVega, TOL);
assertEquals(pvVegaPut.Currency, USD);
assertEquals(pvVegaPut.Amount, -expectedPvVega, NOTIONAL * TOL);
}
//-------------------------------------------------------------------------
public virtual void test_presentValueSensitivityVolatility()
{
for (int i = 0; i < NB_STRIKES; ++i)
{
PointSensitivities computedCall = PRICER.presentValueSensitivityModelParamsVolatility(CALLS[i], RATES_PROVIDER, VOLS).build();
double timeToExpiry = VOLS.relativeTime(EXPIRY);
FxRate forward = FX_PRICER.forwardFxRate(UNDERLYING[i], RATES_PROVIDER);
double forwardRate = forward.fxRate(CURRENCY_PAIR);
double strikeRate = CALLS[i].Strike;
SmileDeltaParameters smileAtTime = VOLS.Smile.smileForExpiry(timeToExpiry);
double[] strikes = smileAtTime.strike(forwardRate).toArray();
double[] vols = smileAtTime.Volatility.toArray();
double df = RATES_PROVIDER.discountFactor(USD, PAY);
double[] weights = this.weights(forwardRate, strikeRate, strikes, timeToExpiry, vols[1]);
double[] vegas = new double[3];
vegas[2] = BlackFormulaRepository.vega(forwardRate, strikeRate, timeToExpiry, vols[1]) * df * NOTIONAL;
for (int j = 0; j < 3; j += 2)
{
vegas[2] -= weights[j] * NOTIONAL *df *BlackFormulaRepository.vega(forwardRate, strikes[j], timeToExpiry, vols[1]);
}
vegas[0] = weights[0] * NOTIONAL *df *BlackFormulaRepository.vega(forwardRate, strikes[0], timeToExpiry, vols[0]);
vegas[1] = weights[2] * NOTIONAL *df *BlackFormulaRepository.vega(forwardRate, strikes[2], timeToExpiry, vols[2]);
double[] expStrikes = new double[] { strikes[0], strikes[2], strikes[1] };
for (int j = 0; j < 3; ++j)
{
FxOptionSensitivity sensi = (FxOptionSensitivity)computedCall.Sensitivities.get(j);
assertEquals(sensi.Sensitivity, vegas[j], TOL * NOTIONAL);
assertEquals(sensi.Strike, expStrikes[j], TOL);
assertEquals(sensi.Forward, forwardRate, TOL);
assertEquals(sensi.Currency, USD);
assertEquals(sensi.CurrencyPair, CURRENCY_PAIR);
assertEquals(sensi.Expiry, timeToExpiry);
}
}
}
//-------------------------------------------------------------------------
public virtual void test_presentValueSensitivityBlackVolatility()
{
FxOptionSensitivity computedCall = (FxOptionSensitivity)PRICER.presentValueSensitivityModelParamsVolatility(CALL_OTM, RATES_PROVIDER, VOLS);
FxOptionSensitivity computedPut = (FxOptionSensitivity)PRICER.presentValueSensitivityModelParamsVolatility(PUT_ITM, RATES_PROVIDER, VOLS);
double timeToExpiry = VOLS.relativeTime(EXPIRY);
double df = RATES_PROVIDER.discountFactor(USD, PAYMENT_DATE);
double forward = PRICER.DiscountingFxSingleProductPricer.forwardFxRate(FX_PRODUCT_HIGH, RATES_PROVIDER).fxRate(CURRENCY_PAIR);
double vol = SMILE_TERM.volatility(timeToExpiry, STRIKE_RATE_HIGH, forward);
FxOptionSensitivity expected = FxOptionSensitivity.of(VOLS.Name, CURRENCY_PAIR, timeToExpiry, STRIKE_RATE_HIGH, forward, USD, -NOTIONAL * df * BlackFormulaRepository.vega(forward, STRIKE_RATE_HIGH, timeToExpiry, vol));
assertTrue(computedCall.build().equalWithTolerance(expected.build(), NOTIONAL * TOL));
assertTrue(computedPut.build().equalWithTolerance(expected.build().multipliedBy(-1d), NOTIONAL * TOL));
}
//-------------------------------------------------------------------------
public virtual void test_presentValueSensitivityVolatility()
{
PointSensitivities pointCaplet = PRICER.presentValueSensitivityModelParamsSabr(CAPLET_LONG, RATES, VOLS).build();
PointSensitivities pointFloorlet = PRICER.presentValueSensitivityModelParamsSabr(FLOORLET_SHORT, RATES, VOLS).build();
double forward = RATES.iborIndexRates(EUR_EURIBOR_3M).rate(RATE_COMP.Observation);
double expiry = VOLS.relativeTime(CAPLET_LONG.FixingDateTime);
ValueDerivatives volSensi = VOLS.Parameters.volatilityAdjoint(expiry, STRIKE, forward);
double df = RATES.discountFactor(EUR, CAPLET_LONG.PaymentDate);
double vegaCaplet = NOTIONAL * df * CAPLET_LONG.YearFraction * BlackFormulaRepository.vega(forward + SHIFT, STRIKE + SHIFT, expiry, volSensi.Value);
double vegaFloorlet = -NOTIONAL *df *CAPLET_LONG.YearFraction *BlackFormulaRepository.vega(forward + SHIFT, STRIKE + SHIFT, expiry, volSensi.Value);
assertSensitivity(pointCaplet, SabrParameterType.ALPHA, vegaCaplet * volSensi.getDerivative(2), TOL);
assertSensitivity(pointCaplet, SabrParameterType.BETA, vegaCaplet * volSensi.getDerivative(3), TOL);
assertSensitivity(pointCaplet, SabrParameterType.RHO, vegaCaplet * volSensi.getDerivative(4), TOL);
assertSensitivity(pointCaplet, SabrParameterType.NU, vegaCaplet * volSensi.getDerivative(5), TOL);
assertSensitivity(pointFloorlet, SabrParameterType.ALPHA, vegaFloorlet * volSensi.getDerivative(2), TOL);
assertSensitivity(pointFloorlet, SabrParameterType.BETA, vegaFloorlet * volSensi.getDerivative(3), TOL);
assertSensitivity(pointFloorlet, SabrParameterType.RHO, vegaFloorlet * volSensi.getDerivative(4), TOL);
assertSensitivity(pointFloorlet, SabrParameterType.NU, vegaFloorlet * volSensi.getDerivative(5), TOL);
PointSensitivities pointCapletVol = PRICER.presentValueSensitivityModelParamsVolatility(CAPLET_LONG, RATES, VOLS).build();
// vol sensitivity in base class
PointSensitivities pointFloorletVol = PRICER.presentValueSensitivityModelParamsVolatility(FLOORLET_SHORT, RATES, VOLS).build();
IborCapletFloorletSensitivity pointCapletVolExp = IborCapletFloorletSensitivity.of(VOLS.Name, expiry, STRIKE, forward, EUR, vegaCaplet);
IborCapletFloorletSensitivity pointFloorletVolExp = IborCapletFloorletSensitivity.of(VOLS.Name, expiry, STRIKE, forward, EUR, vegaFloorlet);
assertEquals(pointCapletVol.Sensitivities.get(0), pointCapletVolExp);
assertEquals(pointFloorletVol.Sensitivities.get(0), pointFloorletVolExp);
}
