/// <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)));
}
/// <summary>
/// Validates that the swaption is single currency cash par-yield.
/// </summary>
/// <param name="swaption"> the swaption </param>
protected internal virtual void validateSwaption(ResolvedSwaption swaption)
{
ArgChecker.isFalse(swaption.Underlying.CrossCurrency, "Underlying swap must be single currency");
ArgChecker.isTrue(swaption.SwaptionSettlement.SettlementType.Equals(SettlementType.CASH), "Swaption must be cash settlement");
CashSwaptionSettlement cashSettle = (CashSwaptionSettlement)swaption.SwaptionSettlement;
ArgChecker.isTrue(cashSettle.Method.Equals(CashSwaptionSettlementMethod.PAR_YIELD), "Cash settlement method must be par yield");
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the numeraire, used to multiply the results.
/// </summary>
/// <param name="swaption"> the swap </param>
/// <param name="fixedLeg"> the fixed leg </param>
/// <param name="forward"> the forward rate </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <returns> the numeraire </returns>
protected internal virtual double calculateNumeraire(ResolvedSwaption swaption, ResolvedSwapLeg fixedLeg, double forward, RatesProvider ratesProvider)
{
double annuityCash = swapPricer.LegPricer.annuityCash(fixedLeg, forward);
CashSwaptionSettlement cashSettlement = (CashSwaptionSettlement)swaption.SwaptionSettlement;
double discountSettle = ratesProvider.discountFactor(fixedLeg.Currency, cashSettlement.SettlementDate);
return(Math.Abs(annuityCash * discountSettle));
}
//-------------------------------------------------------------------------
/// <summary>
/// Computes the implied volatility of the swaption.
/// </summary>
/// <param name="swaption"> the swaption </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="swaptionVolatilities"> the volatilities </param>
/// <returns> the implied volatility associated with the swaption </returns>
public virtual double impliedVolatility(ResolvedSwaption swaption, RatesProvider ratesProvider, SwaptionVolatilities swaptionVolatilities)
{
validate(swaption, ratesProvider, swaptionVolatilities);
double expiry = swaptionVolatilities.relativeTime(swaption.Expiry);
ResolvedSwap underlying = swaption.Underlying;
ResolvedSwapLeg fixedLeg = this.fixedLeg(underlying);
ArgChecker.isTrue(expiry >= 0d, "Option must be before expiry to compute an implied volatility");
double forward = SwapPricer.parRate(underlying, ratesProvider);
double strike = calculateStrike(fixedLeg);
double tenor = swaptionVolatilities.tenor(fixedLeg.StartDate, fixedLeg.EndDate);
return(swaptionVolatilities.volatility(expiry, tenor, strike, forward));
}
//-------------------------------------------------------------------------
/// <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>
/// Computes the implied normal volatility from the present value of a swaption.
/// <para>
/// The guess volatility for the start of the root-finding process is 1%.
///
/// </para>
/// </summary>
/// <param name="swaption"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="dayCount"> the day-count used to estimate the time between valuation date and swaption expiry </param>
/// <param name="presentValue"> the present value of the swaption product </param>
/// <returns> the implied volatility associated with the present value </returns>
public virtual double impliedVolatilityFromPresentValue(ResolvedSwaption swaption, RatesProvider ratesProvider, DayCount dayCount, double presentValue)
{
double sign = swaption.LongShort.sign();
ArgChecker.isTrue(presentValue * sign > 0, "Present value sign must be in line with the option Long/Short flag ");
validateSwaption(swaption);
LocalDate valuationDate = ratesProvider.ValuationDate;
LocalDate expiryDate = swaption.ExpiryDate;
ArgChecker.isTrue(expiryDate.isAfter(valuationDate), "Expiry must be after valuation date to compute an implied volatility");
double expiry = dayCount.yearFraction(valuationDate, expiryDate);
ResolvedSwap underlying = swaption.Underlying;
ResolvedSwapLeg fixedLeg = this.fixedLeg(underlying);
double forward = SwapPricer.parRate(underlying, ratesProvider);
double numeraire = calculateNumeraire(swaption, fixedLeg, forward, ratesProvider);
double strike = calculateStrike(fixedLeg);
PutCall putCall = PutCall.ofPut(fixedLeg.PayReceive.Receive);
return(NormalFormulaRepository.impliedVolatility(Math.Abs(presentValue), forward, strike, expiry, 0.01, numeraire, putCall));
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the present value of the swaption.
/// <para>
/// The result is expressed using the currency of the swaption.
///
/// </para>
/// </summary>
/// <param name="swaption"> the swaption </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="swaptionVolatilities"> the volatilities </param>
/// <returns> the present value </returns>
public virtual CurrencyAmount presentValue(ResolvedSwaption swaption, RatesProvider ratesProvider, SwaptionVolatilities swaptionVolatilities)
{
validate(swaption, ratesProvider, swaptionVolatilities);
double expiry = swaptionVolatilities.relativeTime(swaption.Expiry);
ResolvedSwap underlying = swaption.Underlying;
ResolvedSwapLeg fixedLeg = this.fixedLeg(underlying);
if (expiry < 0d)
{ // Option has expired already
return(CurrencyAmount.of(fixedLeg.Currency, 0d));
}
double forward = swapPricer.parRate(underlying, ratesProvider);
double numeraire = calculateNumeraire(swaption, fixedLeg, forward, ratesProvider);
double strike = calculateStrike(fixedLeg);
double tenor = swaptionVolatilities.tenor(fixedLeg.StartDate, fixedLeg.EndDate);
double volatility = swaptionVolatilities.volatility(expiry, tenor, strike, forward);
PutCall putCall = PutCall.ofPut(fixedLeg.PayReceive.Receive);
double price = numeraire * swaptionVolatilities.price(expiry, tenor, putCall, strike, forward, volatility);
return(CurrencyAmount.of(fixedLeg.Currency, price * swaption.LongShort.sign()));
}
//-------------------------------------------------------------------------
/// <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 present value sensitivity of the swaption to the rate curves.
/// <para>
/// The present value sensitivity is computed in a "sticky strike" style, i.e. the sensitivity to the
/// curve nodes with the volatility at the swaption strike unchanged. This sensitivity does not include a potential
/// change of volatility due to the implicit change of forward rate or moneyness.
///
/// </para>
/// </summary>
/// <param name="swaption"> the swaption </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 presentValueSensitivityRatesStickyStrike(ResolvedSwaption swaption, RatesProvider ratesProvider, SwaptionVolatilities swaptionVolatilities)
{
validate(swaption, ratesProvider, swaptionVolatilities);
double expiry = swaptionVolatilities.relativeTime(swaption.Expiry);
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 volatility = swaptionVolatilities.volatility(expiry, tenor, strike, forward);
PutCall putCall = PutCall.ofPut(fixedLeg.PayReceive.Receive);
double price = swaptionVolatilities.price(expiry, tenor, putCall, strike, forward, volatility);
double delta = swaptionVolatilities.priceDelta(expiry, tenor, putCall, strike, forward, volatility);
// Backward sweep
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 + annuityCashDr * price)).combinedWith(discountSettleSensi.multipliedBy(sign * annuityCash * price)));
}
//-------------------------------------------------------------------------
/// <summary>
/// Computes the currency exposure of the swaption.
/// <para>
/// This is equivalent to the present value of the swaption.
///
/// </para>
/// </summary>
/// <param name="swaption"> the swaption </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="swaptionVolatilities"> the volatilities </param>
/// <returns> the currency exposure </returns>
public virtual MultiCurrencyAmount currencyExposure(ResolvedSwaption swaption, RatesProvider ratesProvider, SwaptionVolatilities swaptionVolatilities)
{
return(MultiCurrencyAmount.of(presentValue(swaption, ratesProvider, swaptionVolatilities)));
}
//-------------------------------------------------------------------------
/// <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 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 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)));
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the present value sensitivity of the swaption to the rate curves.
/// <para>
/// The present value sensitivity is computed in a "sticky strike" style, i.e. the sensitivity to the
/// curve nodes with the volatility at the swaption strike unchanged. This sensitivity does not include a potential
/// change of volatility due to the implicit change of forward rate or moneyness.
///
/// </para>
/// </summary>
/// <param name="swaption"> the swaption </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 presentValueSensitivityRatesStickyStrike(ResolvedSwaption swaption, RatesProvider ratesProvider, SwaptionVolatilities swaptionVolatilities)
{
validate(swaption, ratesProvider, swaptionVolatilities);
double expiry = swaptionVolatilities.relativeTime(swaption.Expiry);
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 volatility = swaptionVolatilities.volatility(expiry, tenor, strike, forward);
PutCall putCall = PutCall.ofPut(fixedLeg.PayReceive.Receive);
double price = swaptionVolatilities.price(expiry, tenor, putCall, strike, forward, volatility);
double delta = swaptionVolatilities.priceDelta(expiry, tenor, putCall, strike, forward, volatility);
// Backward sweep
PointSensitivityBuilder pvbpDr = SwapPricer.LegPricer.pvbpSensitivity(fixedLeg, ratesProvider);
PointSensitivityBuilder forwardDr = SwapPricer.parRateSensitivity(underlying, ratesProvider);
double sign = swaption.LongShort.sign();
return(pvbpDr.multipliedBy(price * sign * Math.Sign(pvbp)).combinedWith(forwardDr.multipliedBy(delta * Math.Abs(pvbp) * sign)));
}
//-------------------------------------------------------------------------
// 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>
/// Validates that the rates and volatilities providers are coherent
/// and that the swaption is single currency cash par-yield.
/// </summary>
/// <param name="swaption"> the swaption </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="swaptionVolatilities"> the volatilities </param>
protected internal virtual void validate(ResolvedSwaption swaption, RatesProvider ratesProvider, SwaptionVolatilities swaptionVolatilities)
{
ArgChecker.isTrue(swaptionVolatilities.ValuationDate.Equals(ratesProvider.ValuationDate), "Volatility and rate data must be for the same date");
validateSwaption(swaption);
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the present value sensitivity to the implied volatility of the swaption.
/// <para>
/// The sensitivity to the implied volatility is also called vega.
///
/// </para>
/// </summary>
/// <param name="swaption"> the swaption </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="swaptionVolatilities"> the volatilities </param>
/// <returns> the point sensitivity to the volatility </returns>
public virtual SwaptionSensitivity presentValueSensitivityModelParamsVolatility(ResolvedSwaption swaption, RatesProvider ratesProvider, SwaptionVolatilities 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 pvbp = SwapPricer.LegPricer.pvbp(fixedLeg, ratesProvider);
double strike = SwapPricer.LegPricer.couponEquivalent(fixedLeg, ratesProvider, pvbp);
if (expiry < 0d)
{ // Option has expired already
return(SwaptionSensitivity.of(swaptionVolatilities.Name, expiry, tenor, strike, 0d, fixedLeg.Currency, 0d));
}
double forward = SwapPricer.parRate(underlying, ratesProvider);
double numeraire = Math.Abs(pvbp);
double volatility = swaptionVolatilities.volatility(expiry, tenor, strike, forward);
PutCall putCall = PutCall.ofPut(fixedLeg.PayReceive.Receive);
double vega = numeraire * swaptionVolatilities.priceVega(expiry, tenor, putCall, strike, forward, volatility);
return(SwaptionSensitivity.of(swaptionVolatilities.Name, expiry, tenor, strike, forward, fixedLeg.Currency, vega * swaption.LongShort.sign()));
}
/// <summary>
/// Validates that the swaption is single currency physical.
/// </summary>
/// <param name="swaption"> the swaption </param>
protected internal virtual void validateSwaption(ResolvedSwaption swaption)
{
ArgChecker.isFalse(swaption.Underlying.CrossCurrency, "Underlying swap must be single currency");
ArgChecker.isTrue(swaption.SwaptionSettlement.SettlementType.Equals(SettlementType.PHYSICAL), "Swaption must be physical settlement");
}
//-------------------------------------------------------------------------
/// <summary>
/// Runs the calibration of SABR on swaptions and print on the console the present value, bucketed PV01 and
/// the bucketed Vega of a 18M x 4Y swaption.
/// </summary>
/// <param name="args"> -s to use the spares data </param>
public static void Main(string[] args)
{
long start, end;
// Swaption description
BuySell payer = BuySell.BUY;
Period expiry = Period.ofMonths(18);
double notional = 1_000_000;
double strike = 0.0100;
Tenor tenor = Tenor.TENOR_4Y;
LocalDate expiryDate = EUR_FIXED_1Y_EURIBOR_6M.FloatingLeg.StartDateBusinessDayAdjustment.adjust(CALIBRATION_DATE.plus(expiry), REF_DATA);
SwapTrade underlying = EUR_FIXED_1Y_EURIBOR_6M.createTrade(expiryDate, tenor, payer, notional, strike, REF_DATA);
Swaption swaption = Swaption.builder().expiryDate(AdjustableDate.of(expiryDate)).expiryTime(LocalTime.of(11, 0x0)).expiryZone(ZoneId.of("Europe/Berlin")).underlying(underlying.Product).longShort(LongShort.LONG).swaptionSettlement(PhysicalSwaptionSettlement.DEFAULT).build();
ResolvedSwaption resolvedSwaption = swaption.resolve(REF_DATA);
// select data
TenorRawOptionData data = DATA_FULL;
if (args.Length > 0)
{
if (args[0].Equals("-s"))
{
data = DATA_SPARSE;
}
}
start = DateTimeHelper.CurrentUnixTimeMillis();
// Curve calibration
RatesProvider multicurve = CALIBRATOR.calibrate(CONFIGS, MARKET_QUOTES, REF_DATA);
end = DateTimeHelper.CurrentUnixTimeMillis();
Console.WriteLine("Curve calibration time: " + (end - start) + " ms.");
// SABR calibration
start = DateTimeHelper.CurrentUnixTimeMillis();
double beta = 0.50;
SurfaceMetadata betaMetadata = DefaultSurfaceMetadata.builder().xValueType(ValueType.YEAR_FRACTION).yValueType(ValueType.YEAR_FRACTION).zValueType(ValueType.SABR_BETA).surfaceName("Beta").build();
Surface betaSurface = ConstantSurface.of(betaMetadata, beta);
double shift = 0.0300;
Surface shiftSurface = ConstantSurface.of("SABR-Shift", shift);
SabrParametersSwaptionVolatilities sabr = SABR_CALIBRATION.calibrateWithFixedBetaAndShift(DEFINITION, CALIBRATION_TIME, data, multicurve, betaSurface, shiftSurface);
end = DateTimeHelper.CurrentUnixTimeMillis();
Console.WriteLine("SABR calibration time: " + (end - start) + " ms.");
// Price and risk
Console.WriteLine("Risk measures: ");
start = DateTimeHelper.CurrentUnixTimeMillis();
CurrencyAmount pv = SWAPTION_PRICER.presentValue(resolvedSwaption, multicurve, sabr);
Console.WriteLine(" |-> PV: " + pv.ToString());
PointSensitivities deltaPts = SWAPTION_PRICER.presentValueSensitivityRatesStickyModel(resolvedSwaption, multicurve, sabr).build();
CurrencyParameterSensitivities deltaBucketed = multicurve.parameterSensitivity(deltaPts);
Console.WriteLine(" |-> Delta bucketed: " + deltaBucketed.ToString());
PointSensitivities vegaPts = SWAPTION_PRICER.presentValueSensitivityModelParamsSabr(resolvedSwaption, multicurve, sabr).build();
Console.WriteLine(" |-> Vega point: " + vegaPts.ToString());
CurrencyParameterSensitivities vegaBucketed = sabr.parameterSensitivity(vegaPts);
for (int i = 0; i < vegaBucketed.size(); i++)
{
Console.WriteLine(" |-> Vega bucketed: " + vegaBucketed.Sensitivities.get(i));
}
end = DateTimeHelper.CurrentUnixTimeMillis();
Console.WriteLine("PV and risk time: " + (end - start) + " ms.");
}