//-------------------------------------------------------------------------
public virtual void test_presentValueSensitivityHullWhiteParameter()
{
DoubleArray computedRec = PRICER.presentValueSensitivityModelParamsHullWhite(SWAPTION_REC_LONG, RATE_PROVIDER, HW_PROVIDER);
DoubleArray computedPay = PRICER.presentValueSensitivityModelParamsHullWhite(SWAPTION_PAY_SHORT, RATE_PROVIDER, HW_PROVIDER);
DoubleArray vols = HW_PROVIDER.Parameters.Volatility;
int size = vols.size();
double[] expectedRec = new double[size];
double[] expectedPay = new double[size];
for (int i = 0; i < size; ++i)
{
double[] volsUp = vols.toArray();
double[] volsDw = vols.toArray();
volsUp[i] += FD_TOL;
volsDw[i] -= FD_TOL;
HullWhiteOneFactorPiecewiseConstantParameters paramsUp = HullWhiteOneFactorPiecewiseConstantParameters.of(HW_PROVIDER.Parameters.MeanReversion, DoubleArray.copyOf(volsUp), HW_PROVIDER.Parameters.VolatilityTime.subArray(1, size));
HullWhiteOneFactorPiecewiseConstantParameters paramsDw = HullWhiteOneFactorPiecewiseConstantParameters.of(HW_PROVIDER.Parameters.MeanReversion, DoubleArray.copyOf(volsDw), HW_PROVIDER.Parameters.VolatilityTime.subArray(1, size));
HullWhiteOneFactorPiecewiseConstantParametersProvider provUp = HullWhiteOneFactorPiecewiseConstantParametersProvider.of(paramsUp, HW_PROVIDER.DayCount, HW_PROVIDER.ValuationDateTime);
HullWhiteOneFactorPiecewiseConstantParametersProvider provDw = HullWhiteOneFactorPiecewiseConstantParametersProvider.of(paramsDw, HW_PROVIDER.DayCount, HW_PROVIDER.ValuationDateTime);
expectedRec[i] = 0.5 * (PRICER.presentValue(SWAPTION_REC_LONG, RATE_PROVIDER, provUp).Amount - PRICER.presentValue(SWAPTION_REC_LONG, RATE_PROVIDER, provDw).Amount) / FD_TOL;
expectedPay[i] = 0.5 * (PRICER.presentValue(SWAPTION_PAY_SHORT, RATE_PROVIDER, provUp).Amount - PRICER.presentValue(SWAPTION_PAY_SHORT, RATE_PROVIDER, provDw).Amount) / FD_TOL;
}
assertTrue(DoubleArrayMath.fuzzyEquals(computedRec.toArray(), expectedRec, NOTIONAL * FD_TOL));
assertTrue(DoubleArrayMath.fuzzyEquals(computedPay.toArray(), expectedPay, NOTIONAL * FD_TOL));
}
// handling short time to expiry
private double computeKappa(HullWhiteOneFactorPiecewiseConstantParametersProvider hwProvider, double[] discountedCashFlow, double[] alpha, double omega)
{
double kappa = 0d;
if (DoubleArrayMath.fuzzyEqualsZero(alpha, SMALL))
{ // threshold coherent to rootfinder in kappa computation
double totalPv = DoubleArrayMath.sum(discountedCashFlow);
kappa = totalPv * omega > 0d ? double.PositiveInfinity : double.NegativeInfinity;
}
else
{
kappa = hwProvider.Model.kappa(DoubleArray.ofUnsafe(discountedCashFlow), DoubleArray.ofUnsafe(alpha));
}
return(kappa);
}
/// <summary>
/// Calculates the present value of the swaption product.
/// <para>
/// The result is expressed using the currency of the swapion.
///
/// </para>
/// </summary>
/// <param name="swaption"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="hwProvider"> the Hull-White model parameter provider </param>
/// <returns> the present value </returns>
public virtual CurrencyAmount presentValue(ResolvedSwaption swaption, RatesProvider ratesProvider, HullWhiteOneFactorPiecewiseConstantParametersProvider hwProvider)
{
validate(swaption, ratesProvider, hwProvider);
ResolvedSwap swap = swaption.Underlying;
LocalDate expiryDate = swaption.ExpiryDate;
if (expiryDate.isBefore(ratesProvider.ValuationDate))
{ // Option has expired already
return(CurrencyAmount.of(swap.Legs.get(0).Currency, 0d));
}
ResolvedSwapLeg cashFlowEquiv = CashFlowEquivalentCalculator.cashFlowEquivalentSwap(swap, ratesProvider);
int nPayments = cashFlowEquiv.PaymentEvents.size();
double[] alpha = new double[nPayments];
double[] discountedCashFlow = new double[nPayments];
for (int loopcf = 0; loopcf < nPayments; loopcf++)
{
NotionalExchange payment = (NotionalExchange)cashFlowEquiv.PaymentEvents.get(loopcf);
LocalDate maturityDate = payment.PaymentDate;
alpha[loopcf] = hwProvider.alpha(ratesProvider.ValuationDate, expiryDate, expiryDate, maturityDate);
discountedCashFlow[loopcf] = paymentPricer.presentValueAmount(payment.Payment, ratesProvider);
}
double omega = (swap.getLegs(SwapLegType.FIXED).get(0).PayReceive.Pay ? -1d : 1d);
double kappa = computeKappa(hwProvider, discountedCashFlow, alpha, omega);
double pv = 0.0;
for (int loopcf = 0; loopcf < nPayments; loopcf++)
{
pv += discountedCashFlow[loopcf] * NORMAL.getCDF(omega * (kappa + alpha[loopcf]));
}
return(CurrencyAmount.of(cashFlowEquiv.Currency, pv * (swaption.LongShort.Long ? 1d : -1d)));
}
//-------------------------------------------------------------------------
// validate that the rates and volatilities providers are coherent
private void validate(ResolvedSwaption swaption, RatesProvider ratesProvider, HullWhiteOneFactorPiecewiseConstantParametersProvider hwProvider)
{
ArgChecker.isTrue(hwProvider.ValuationDateTime.toLocalDate().Equals(ratesProvider.ValuationDate), "Hull-White model data and rate data should be for the same date");
ArgChecker.isFalse(swaption.Underlying.CrossCurrency, "underlying swap should be single currency");
ArgChecker.isTrue(swaption.SwaptionSettlement.SettlementType.Equals(SettlementType.PHYSICAL), "swaption should be physical settlement");
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the present value sensitivity to piecewise constant volatility parameters of the Hull-White model.
/// </summary>
/// <param name="swaption"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="hwProvider"> the Hull-White model parameter provider </param>
/// <returns> the present value Hull-White model parameter sensitivity of the swaption product </returns>
public virtual DoubleArray presentValueSensitivityModelParamsHullWhite(ResolvedSwaption swaption, RatesProvider ratesProvider, HullWhiteOneFactorPiecewiseConstantParametersProvider hwProvider)
{
validate(swaption, ratesProvider, hwProvider);
ResolvedSwap swap = swaption.Underlying;
LocalDate expiryDate = swaption.ExpiryDate;
if (expiryDate.isBefore(ratesProvider.ValuationDate))
{ // Option has expired already
return(DoubleArray.EMPTY);
}
ResolvedSwapLeg cashFlowEquiv = CashFlowEquivalentCalculator.cashFlowEquivalentSwap(swap, ratesProvider);
int nPayments = cashFlowEquiv.PaymentEvents.size();
double[] alpha = new double[nPayments];
double[][] alphaAdjoint = new double[nPayments][];
double[] discountedCashFlow = new double[nPayments];
for (int loopcf = 0; loopcf < nPayments; loopcf++)
{
NotionalExchange payment = (NotionalExchange)cashFlowEquiv.PaymentEvents.get(loopcf);
ValueDerivatives valueDeriv = hwProvider.alphaAdjoint(ratesProvider.ValuationDate, expiryDate, expiryDate, payment.PaymentDate);
alpha[loopcf] = valueDeriv.Value;
alphaAdjoint[loopcf] = valueDeriv.Derivatives.toArray();
discountedCashFlow[loopcf] = paymentPricer.presentValueAmount(payment.Payment, ratesProvider);
}
double omega = (swap.getLegs(SwapLegType.FIXED).get(0).PayReceive.Pay ? -1d : 1d);
double kappa = computeKappa(hwProvider, discountedCashFlow, alpha, omega);
int nParams = alphaAdjoint[0].Length;
if (Math.Abs(kappa) > 1d / SMALL)
{ // decays exponentially
return(DoubleArray.filled(nParams));
}
double[] pvSensi = new double[nParams];
double sign = (swaption.LongShort.Long ? 1d : -1d);
for (int i = 0; i < nParams; ++i)
{
for (int loopcf = 0; loopcf < nPayments; loopcf++)
{
pvSensi[i] += sign * discountedCashFlow[loopcf] * NORMAL.getPDF(omega * (kappa + alpha[loopcf])) * omega * alphaAdjoint[loopcf][i];
}
}
return(DoubleArray.ofUnsafe(pvSensi));
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the present value sensitivity of the swaption product.
/// <para>
/// The present value sensitivity of the product is the sensitivity of the present value to
/// the underlying curves.
///
/// </para>
/// </summary>
/// <param name="swaption"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="hwProvider"> the Hull-White model parameter provider </param>
/// <returns> the point sensitivity to the rate curves </returns>
public virtual PointSensitivityBuilder presentValueSensitivityRates(ResolvedSwaption swaption, RatesProvider ratesProvider, HullWhiteOneFactorPiecewiseConstantParametersProvider hwProvider)
{
validate(swaption, ratesProvider, hwProvider);
ResolvedSwap swap = swaption.Underlying;
LocalDate expiryDate = swaption.ExpiryDate;
if (expiryDate.isBefore(ratesProvider.ValuationDate))
{ // Option has expired already
return(PointSensitivityBuilder.none());
}
ImmutableMap <Payment, PointSensitivityBuilder> cashFlowEquivSensi = CashFlowEquivalentCalculator.cashFlowEquivalentAndSensitivitySwap(swap, ratesProvider);
ImmutableList <Payment> list = cashFlowEquivSensi.Keys.asList();
ImmutableList <PointSensitivityBuilder> listSensi = cashFlowEquivSensi.values().asList();
int nPayments = list.size();
double[] alpha = new double[nPayments];
double[] discountedCashFlow = new double[nPayments];
for (int loopcf = 0; loopcf < nPayments; loopcf++)
{
Payment payment = list.get(loopcf);
alpha[loopcf] = hwProvider.alpha(ratesProvider.ValuationDate, expiryDate, expiryDate, payment.Date);
discountedCashFlow[loopcf] = paymentPricer.presentValueAmount(payment, ratesProvider);
}
double omega = (swap.getLegs(SwapLegType.FIXED).get(0).PayReceive.Pay ? -1d : 1d);
double kappa = computeKappa(hwProvider, discountedCashFlow, alpha, omega);
PointSensitivityBuilder point = PointSensitivityBuilder.none();
for (int loopcf = 0; loopcf < nPayments; loopcf++)
{
Payment payment = list.get(loopcf);
double cdf = NORMAL.getCDF(omega * (kappa + alpha[loopcf]));
point = point.combinedWith(paymentPricer.presentValueSensitivity(payment, ratesProvider).multipliedBy(cdf));
if (!listSensi.get(loopcf).Equals(PointSensitivityBuilder.none()))
{
point = point.combinedWith(listSensi.get(loopcf).multipliedBy(cdf * ratesProvider.discountFactor(payment.Currency, payment.Date)));
}
}
return(swaption.LongShort.Long ? point : point.multipliedBy(-1d));
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the currency exposure of the swaption product.
/// </summary>
/// <param name="swaption"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="hwProvider"> the Hull-White model parameter provider </param>
/// <returns> the currency exposure </returns>
public virtual MultiCurrencyAmount currencyExposure(ResolvedSwaption swaption, RatesProvider ratesProvider, HullWhiteOneFactorPiecewiseConstantParametersProvider hwProvider)
{
return(MultiCurrencyAmount.of(presentValue(swaption, ratesProvider, hwProvider)));
}
