/// <summary>
/// Calculates the par spread curve sensitivity for a swap.
/// <para>
/// The par spread is the common spread on all payments of the first leg for which the total swap present value is 0.
/// </para>
/// <para>
/// The par spread is computed with respect to the first leg. For that leg, all the payments have a unique
/// accrual period (no compounding) and no FX reset.
///
/// </para>
/// </summary>
/// <param name="swap"> the product </param>
/// <param name="provider"> the rates provider </param>
/// <returns> the par spread curve sensitivity of the swap product </returns>
public virtual PointSensitivityBuilder parSpreadSensitivity(ResolvedSwap swap, RatesProvider provider)
{
ResolvedSwapLeg referenceLeg = swap.Legs.get(0);
Currency ccyReferenceLeg = referenceLeg.Currency;
double convertedPv = presentValue(swap, ccyReferenceLeg, provider).Amount;
PointSensitivityBuilder convertedPvDr = presentValueSensitivity(swap, ccyReferenceLeg, provider);
// try one payment compounding, typically for inflation swaps
Triple <bool, int, double> fixedCompounded = checkFixedCompounded(referenceLeg);
if (fixedCompounded.First)
{
double df = provider.discountFactor(ccyReferenceLeg, referenceLeg.PaymentPeriods.get(0).PaymentDate);
PointSensitivityBuilder dfDr = provider.discountFactors(ccyReferenceLeg).zeroRatePointSensitivity(referenceLeg.PaymentPeriods.get(0).PaymentDate);
double referenceConvertedPv = legPricer.presentValue(referenceLeg, provider).Amount;
PointSensitivityBuilder referenceConvertedPvDr = legPricer.presentValueSensitivity(referenceLeg, provider);
double notional = ((RatePaymentPeriod)referenceLeg.PaymentPeriods.get(0)).Notional;
PointSensitivityBuilder dParSpreadDr = convertedPvDr.combinedWith(referenceConvertedPvDr.multipliedBy(-1)).multipliedBy(-1.0d / (df * notional)).combinedWith(dfDr.multipliedBy((convertedPv - referenceConvertedPv) / (df * df * notional))).multipliedBy(1.0d / fixedCompounded.Second * Math.Pow(-(convertedPv - referenceConvertedPv) / (df * notional) + 1.0d, 1.0d / fixedCompounded.Second - 1.0d));
return(dParSpreadDr);
}
double pvbp = legPricer.pvbp(referenceLeg, provider);
// Backward sweep
double convertedPvBar = -1d / pvbp;
double pvbpBar = convertedPv / (pvbp * pvbp);
PointSensitivityBuilder pvbpDr = legPricer.pvbpSensitivity(referenceLeg, provider);
return(convertedPvDr.multipliedBy(convertedPvBar).combinedWith(pvbpDr.multipliedBy(pvbpBar)));
}
//-------------------------------------------------------------------------
public virtual void test_combinedWith()
{
PointSensitivityBuilder @base = PointSensitivityBuilder.none();
PointSensitivityBuilder ibor = DummyPointSensitivity.of(GBP, date(2015, 6, 30), 2.0d);
assertSame(@base.combinedWith(ibor), ibor); // returns other
}
private PointSensitivityBuilder rateForwardSensitivity(OvernightAveragedRateComputation computation, OvernightIndexRates rates)
{
OvernightIndex index = computation.Index;
HolidayCalendar calendar = computation.FixingCalendar;
LocalDate startFixingDate = computation.StartDate;
LocalDate endFixingDateP1 = computation.EndDate;
LocalDate endFixingDate = calendar.previous(endFixingDateP1);
LocalDate onRateEndDate = computation.calculateMaturityFromFixing(endFixingDate);
LocalDate onRateStartDate = computation.calculateEffectiveFromFixing(startFixingDate);
LocalDate lastNonCutOffMatDate = onRateEndDate;
int cutoffOffset = computation.RateCutOffDays > 1 ? computation.RateCutOffDays : 1;
PointSensitivityBuilder combinedPointSensitivityBuilder = PointSensitivityBuilder.none();
double accrualFactorTotal = index.DayCount.yearFraction(onRateStartDate, onRateEndDate);
if (cutoffOffset > 1)
{ // Cut-off period
IList <double> noCutOffAccrualFactorList = new List <double>();
LocalDate currentFixingDate = endFixingDateP1;
LocalDate cutOffEffectiveDate;
for (int i = 0; i < cutoffOffset; i++)
{
currentFixingDate = calendar.previous(currentFixingDate);
cutOffEffectiveDate = computation.calculateEffectiveFromFixing(currentFixingDate);
lastNonCutOffMatDate = computation.calculateMaturityFromEffective(cutOffEffectiveDate);
double accrualFactor = index.DayCount.yearFraction(cutOffEffectiveDate, lastNonCutOffMatDate);
noCutOffAccrualFactorList.Add(accrualFactor);
}
OvernightIndexObservation lastIndexObs = computation.observeOn(currentFixingDate);
PointSensitivityBuilder forwardRateCutOffSensitivity = rates.ratePointSensitivity(lastIndexObs);
double totalAccrualFactor = 0.0;
for (int i = 0; i < cutoffOffset - 1; i++)
{
totalAccrualFactor += noCutOffAccrualFactorList[i];
}
forwardRateCutOffSensitivity = forwardRateCutOffSensitivity.multipliedBy(totalAccrualFactor);
combinedPointSensitivityBuilder = combinedPointSensitivityBuilder.combinedWith(forwardRateCutOffSensitivity);
}
// Approximated part
OvernightIndexObservation indexObs = computation.observeOn(onRateStartDate);
PointSensitivityBuilder approximatedInterestAndSensitivity = approximatedInterestSensitivity(indexObs, lastNonCutOffMatDate, rates);
combinedPointSensitivityBuilder = combinedPointSensitivityBuilder.combinedWith(approximatedInterestAndSensitivity);
combinedPointSensitivityBuilder = combinedPointSensitivityBuilder.multipliedBy(1.0 / accrualFactorTotal);
// final rate
return(combinedPointSensitivityBuilder);
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the Present Value of a Basis Point curve sensitivity for a fixed swap leg.
/// <para>
/// The Present Value of a Basis Point is the value of the leg when the rate is equal to 1.
/// A better name would be "Present Value of 1".
/// The quantity is also known as "physical annuity" or "level".
/// </para>
/// <para>
/// Each period must not have FX reset or compounding.
/// They must not be of type <seealso cref="KnownAmountSwapPaymentPeriod"/>.
///
/// </para>
/// </summary>
/// <param name="fixedLeg"> the swap fixed leg </param>
/// <param name="provider"> the rates provider </param>
/// <returns> the Present Value of a Basis Point sensitivity to the curves </returns>
public virtual PointSensitivityBuilder pvbpSensitivity(ResolvedSwapLeg fixedLeg, RatesProvider provider)
{
PointSensitivityBuilder builder = PointSensitivityBuilder.none();
foreach (SwapPaymentPeriod period in fixedLeg.PaymentPeriods)
{
builder = builder.combinedWith(paymentPeriodPricer.pvbpSensitivity(period, provider));
}
return(builder);
}
// calculate present or forecast value sensitivity for the swap
private static PointSensitivityBuilder swapValueSensitivity(ResolvedSwap swap, RatesProvider provider, System.Func <ResolvedSwapLeg, RatesProvider, PointSensitivityBuilder> legFn)
{
PointSensitivityBuilder builder = PointSensitivityBuilder.none();
foreach (ResolvedSwapLeg leg in swap.Legs)
{
builder = builder.combinedWith(legFn(leg, provider));
}
return(builder);
}
// calculate present or forecast value sensitivity for a leg
private PointSensitivityBuilder legValueSensitivity(ResolvedSwapLeg leg, RatesProvider provider, System.Func <SwapPaymentPeriod, RatesProvider, PointSensitivityBuilder> periodFn, System.Func <SwapPaymentEvent, RatesProvider, PointSensitivityBuilder> eventFn)
{
PointSensitivityBuilder builder = PointSensitivityBuilder.none();
foreach (SwapPaymentPeriod period in leg.PaymentPeriods)
{
if (!period.PaymentDate.isBefore(provider.ValuationDate))
{
builder = builder.combinedWith(periodFn(period, provider));
}
}
foreach (SwapPaymentEvent @event in leg.PaymentEvents)
{
if ([email protected](provider.ValuationDate))
{
builder = builder.combinedWith(eventFn(@event, provider));
}
}
return(builder);
}
/// <summary>
/// Calculates the present value sensitivity of the swap product converted in a given currency.
/// <para>
/// The present value sensitivity of the product is the sensitivity of the present value to
/// the underlying curves.
///
/// </para>
/// </summary>
/// <param name="swap"> the product </param>
/// <param name="currency"> the currency to convert to </param>
/// <param name="provider"> the rates provider </param>
/// <returns> the present value curve sensitivity of the swap product converted in the given currency </returns>
public virtual PointSensitivityBuilder presentValueSensitivity(ResolvedSwap swap, Currency currency, RatesProvider provider)
{
PointSensitivityBuilder builder = PointSensitivityBuilder.none();
foreach (ResolvedSwapLeg leg in swap.Legs)
{
PointSensitivityBuilder ls = legPricer.presentValueSensitivity(leg, provider);
PointSensitivityBuilder lsConverted = ls.withCurrency(currency).multipliedBy(provider.fxRate(leg.Currency, currency));
builder = builder.combinedWith(lsConverted);
}
return(builder);
}
// Calculate the total rate sensitivity
internal PointSensitivityBuilder calculateRateSensitivity()
{
double factor = pastCompositionFactor() * valuationCompositionFactor() / accrualFactorTotal;
ObjDoublePair <PointSensitivityBuilder> compositionFactorAndSensitivityNonCutoff = this.compositionFactorAndSensitivityNonCutoff();
ObjDoublePair <PointSensitivityBuilder> compositionFactorAndSensitivityCutoff = this.compositionFactorAndSensitivityCutoff();
PointSensitivityBuilder combinedPointSensitivity = compositionFactorAndSensitivityNonCutoff.First.multipliedBy(compositionFactorAndSensitivityCutoff.Second * factor);
combinedPointSensitivity = combinedPointSensitivity.combinedWith(compositionFactorAndSensitivityCutoff.First.multipliedBy(compositionFactorAndSensitivityNonCutoff.Second * factor));
return(combinedPointSensitivity);
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the present value curve sensitivity of the CMS product.
/// <para>
/// The present value sensitivity of the product is the sensitivity of the present value to the underlying curves.
///
/// </para>
/// </summary>
/// <param name="cms"> the CMS product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="swaptionVolatilities"> the swaption volatilities </param>
/// <returns> the present value sensitivity </returns>
public virtual PointSensitivityBuilder presentValueSensitivityRates(ResolvedCms cms, RatesProvider ratesProvider, SabrSwaptionVolatilities swaptionVolatilities)
{
PointSensitivityBuilder pvSensiCmsLeg = cmsLegPricer.presentValueSensitivityRates(cms.CmsLeg, ratesProvider, swaptionVolatilities);
if (!cms.PayLeg.Present)
{
return(pvSensiCmsLeg);
}
PointSensitivityBuilder pvSensiPayLeg = payLegPricer.presentValueSensitivity(cms.PayLeg.get(), ratesProvider);
return(pvSensiCmsLeg.combinedWith(pvSensiPayLeg));
}
// Calculate the total rate sensitivity.
internal PointSensitivityBuilder calculateRateSensitivity()
{
// call these methods to ensure mutable fixedPeriod variable is updated
pastAccumulation();
valuationDateAccumulation();
// calculate sensitivity
PointSensitivityBuilder combinedPointSensitivity = approximatedForwardAccumulationSensitivity();
PointSensitivityBuilder cutOffAccumulationSensitivity = this.cutOffAccumulationSensitivity();
combinedPointSensitivity = combinedPointSensitivity.combinedWith(cutOffAccumulationSensitivity);
combinedPointSensitivity = combinedPointSensitivity.multipliedBy(1.0d / accrualFactorTotal);
return(combinedPointSensitivity);
}
public virtual void test_presentValueSensitivitySabrParameter_afterPay()
{
PointSensitivityBuilder computed = LEG_PRICER.presentValueSensitivityModelParamsSabr(FLOOR_LEG, RATES_PROVIDER_AFTER_PERIOD, VOLATILITIES_AFTER_PERIOD);
PointSensitivityBuilder expected = PointSensitivityBuilder.none();
IList <CmsPeriod> cms = FLOOR_LEG.CmsPeriods;
int size = cms.Count;
for (int i = 0; i < size; ++i)
{
expected = expected.combinedWith(PERIOD_PRICER.presentValueSensitivityModelParamsSabr(cms[i], RATES_PROVIDER_AFTER_PERIOD, VOLATILITIES_AFTER_PERIOD));
}
assertEquals(computed, expected);
}
// calculates the present value curve sensitivity of the periods composing the leg in the currency of the swap leg
internal virtual PointSensitivityBuilder presentValueSensitivityPeriodsInternal(ResolvedSwapLeg leg, RatesProvider provider)
{
PointSensitivityBuilder builder = PointSensitivityBuilder.none();
foreach (SwapPaymentPeriod period in leg.PaymentPeriods)
{
if (!period.PaymentDate.isBefore(provider.ValuationDate))
{
builder = builder.combinedWith(paymentPeriodPricer.presentValueSensitivity(period, provider));
}
}
return(builder);
}
// Accumulated rate sensitivity - cutoff part if not fixed
internal PointSensitivityBuilder cutOffAccumulationSensitivity()
{
PointSensitivityBuilder combinedPointSensitivityBuilder = PointSensitivityBuilder.none();
int nbPeriodNotCutOff = nbPeriods - cutoffOffset + 1;
for (int i = Math.Max(fixedPeriod, nbPeriodNotCutOff); i < nbPeriods; i++)
{
OvernightIndexObservation obs = observations[i];
PointSensitivityBuilder forwardRateSensitivity = rates.ratePointSensitivity(obs).multipliedBy(obs.YearFraction);
combinedPointSensitivityBuilder = combinedPointSensitivityBuilder.combinedWith(forwardRateSensitivity);
}
return(combinedPointSensitivityBuilder);
}
//-------------------------------------------------------------------------
/// <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));
}
internal virtual PointSensitivityBuilder riskyAnnuitySensitivity(ResolvedCds cds, CreditDiscountFactors discountFactors, LegalEntitySurvivalProbabilities survivalProbabilities, LocalDate referenceDate, LocalDate stepinDate, LocalDate effectiveStartDate)
{
double pv = 0d;
PointSensitivityBuilder pvSensi = PointSensitivityBuilder.none();
foreach (CreditCouponPaymentPeriod coupon in cds.PaymentPeriods)
{
if (stepinDate.isBefore(coupon.EndDate))
{
double q = survivalProbabilities.survivalProbability(coupon.EffectiveEndDate);
PointSensitivityBuilder qSensi = survivalProbabilities.zeroRatePointSensitivity(coupon.EffectiveEndDate);
double p = discountFactors.discountFactor(coupon.PaymentDate);
PointSensitivityBuilder pSensi = discountFactors.zeroRatePointSensitivity(coupon.PaymentDate);
pv += coupon.YearFraction * p * q;
pvSensi = pvSensi.combinedWith(pSensi.multipliedBy(coupon.YearFraction * q).combinedWith(qSensi.multipliedBy(coupon.YearFraction * p)));
}
}
if (cds.PaymentOnDefault.AccruedInterest)
{
// This is needed so that the code is consistent with ISDA C when the Markit `fix' is used.
LocalDate start = cds.PaymentPeriods.size() == 1 ? effectiveStartDate : cds.AccrualStartDate;
DoubleArray integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(discountFactors.relativeYearFraction(start), discountFactors.relativeYearFraction(cds.ProtectionEndDate), discountFactors.ParameterKeys, survivalProbabilities.ParameterKeys);
foreach (CreditCouponPaymentPeriod coupon in cds.PaymentPeriods)
{
Pair <double, PointSensitivityBuilder> pvAndSensi = singlePeriodAccrualOnDefaultSensitivity(coupon, effectiveStartDate, integrationSchedule, discountFactors, survivalProbabilities);
pv += pvAndSensi.First;
pvSensi = pvSensi.combinedWith(pvAndSensi.Second);
}
}
double df = discountFactors.discountFactor(referenceDate);
PointSensitivityBuilder dfSensi = discountFactors.zeroRatePointSensitivity(referenceDate).multipliedBy(-pv / (df * df));
pvSensi = pvSensi.multipliedBy(1d / df);
return(dfSensi.combinedWith(pvSensi));
}
/// <summary>
/// Calculates the par spread sensitivity of the product.
/// <para>
/// The par spread sensitivity of the product is the sensitivity of par spread to the underlying curves.
/// The resulting sensitivity is based on the currency of the CDS product.
///
/// </para>
/// </summary>
/// <param name="cds"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="referenceDate"> the reference date </param>
/// <param name="refData"> the reference data </param>
/// <returns> the par spread </returns>
public virtual PointSensitivityBuilder parSpreadSensitivity(ResolvedCds cds, CreditRatesProvider ratesProvider, LocalDate referenceDate, ReferenceData refData)
{
ArgChecker.isTrue(cds.ProtectionEndDate.isAfter(ratesProvider.ValuationDate), "CDS already expired");
LocalDate stepinDate = cds.StepinDateOffset.adjust(ratesProvider.ValuationDate, refData);
LocalDate effectiveStartDate = cds.calculateEffectiveStartDate(stepinDate);
double recoveryRate = this.recoveryRate(cds, ratesProvider);
Pair <CreditDiscountFactors, LegalEntitySurvivalProbabilities> rates = reduceDiscountFactors(cds, ratesProvider);
double protectionLeg = this.protectionLeg(cds, rates.First, rates.Second, referenceDate, effectiveStartDate, recoveryRate);
double riskyAnnuityInv = 1d / riskyAnnuity(cds, rates.First, rates.Second, referenceDate, stepinDate, effectiveStartDate, PriceType.CLEAN);
PointSensitivityBuilder protectionLegSensi = protectionLegSensitivity(cds, rates.First, rates.Second, referenceDate, effectiveStartDate, recoveryRate).multipliedBy(riskyAnnuityInv);
PointSensitivityBuilder riskyAnnuitySensi = riskyAnnuitySensitivity(cds, rates.First, rates.Second, referenceDate, stepinDate, effectiveStartDate).multipliedBy(-protectionLeg * riskyAnnuityInv * riskyAnnuityInv);
return(protectionLegSensi.combinedWith(riskyAnnuitySensi));
}
/// <summary>
/// Calculates the present value sensitivity of the foreign exchange vanilla option product.
/// <para>
/// The present value sensitivity of the product is the sensitivity of <seealso cref="#presentValue"/> to
/// the underlying curves.
/// </para>
/// <para>
/// The volatility is fixed in this sensitivity computation.
///
/// </para>
/// </summary>
/// <param name="option"> the option product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="volatilities"> the Black volatility provider </param>
/// <returns> the present value curve sensitivity of the product </returns>
public virtual PointSensitivities presentValueSensitivityRatesStickyStrike(ResolvedFxVanillaOption option, RatesProvider ratesProvider, BlackFxOptionVolatilities volatilities)
{
if (volatilities.relativeTime(option.Expiry) < 0d)
{
return(PointSensitivities.empty());
}
ResolvedFxSingle underlying = option.Underlying;
double fwdDelta = undiscountedDelta(option, ratesProvider, volatilities);
double discountFactor = ratesProvider.discountFactor(option.CounterCurrency, underlying.PaymentDate);
double notional = signedNotional(option);
PointSensitivityBuilder fwdSensi = fxPricer.forwardFxRatePointSensitivity(option.PutCall.Call ? underlying : underlying.inverse(), ratesProvider).multipliedBy(notional * discountFactor * fwdDelta);
double fwdPrice = undiscountedPrice(option, ratesProvider, volatilities);
PointSensitivityBuilder dscSensi = ratesProvider.discountFactors(option.CounterCurrency).zeroRatePointSensitivity(underlying.PaymentDate).multipliedBy(notional * fwdPrice);
return(fwdSensi.combinedWith(dscSensi).build().convertedTo(option.CounterCurrency, ratesProvider));
}
/// <summary>
/// Calculates the price sensitivity of the product.
/// <para>
/// The price sensitivity of the product is the sensitivity of price to the underlying curves.
///
/// </para>
/// </summary>
/// <param name="cds"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="referenceDate"> the reference date </param>
/// <param name="refData"> the reference data </param>
/// <returns> the present value sensitivity </returns>
public virtual PointSensitivityBuilder priceSensitivity(ResolvedCds cds, CreditRatesProvider ratesProvider, LocalDate referenceDate, ReferenceData refData)
{
if (isExpired(cds, ratesProvider))
{
return(PointSensitivityBuilder.none());
}
LocalDate stepinDate = cds.StepinDateOffset.adjust(ratesProvider.ValuationDate, refData);
LocalDate effectiveStartDate = cds.calculateEffectiveStartDate(stepinDate);
double recoveryRate = this.recoveryRate(cds, ratesProvider);
Pair <CreditDiscountFactors, LegalEntitySurvivalProbabilities> rates = reduceDiscountFactors(cds, ratesProvider);
PointSensitivityBuilder protectionLegSensi = protectionLegSensitivity(cds, rates.First, rates.Second, referenceDate, effectiveStartDate, recoveryRate);
PointSensitivityBuilder riskyAnnuitySensi = riskyAnnuitySensitivity(cds, rates.First, rates.Second, referenceDate, stepinDate, effectiveStartDate).multipliedBy(-cds.FixedRate);
return(protectionLegSensi.combinedWith(riskyAnnuitySensi));
}
//-------------------------------------------------------------------------
/// <summary>
/// Calculates the present value sensitivity of the foreign exchange vanilla option product.
/// <para>
/// The present value sensitivity of the product is the sensitivity of <seealso cref="#presentValue"/> to
/// the underlying curves.
/// </para>
/// <para>
/// The implied strikes and weights are fixed in this sensitivity computation.
///
/// </para>
/// </summary>
/// <param name="option"> the option product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="volatilities"> the Black volatility provider </param>
/// <returns> the present value curve sensitivity of the product </returns>
public virtual PointSensitivityBuilder presentValueSensitivityRatesStickyStrike(ResolvedFxVanillaOption option, RatesProvider ratesProvider, BlackFxOptionSmileVolatilities volatilities)
{
validate(ratesProvider, volatilities);
double timeToExpiry = volatilities.relativeTime(option.Expiry);
if (timeToExpiry <= 0d)
{
return(PointSensitivityBuilder.none());
}
ResolvedFxSingle underlyingFx = option.Underlying;
Currency ccyCounter = option.CounterCurrency;
double df = ratesProvider.discountFactor(ccyCounter, underlyingFx.PaymentDate);
FxRate forward = fxPricer.forwardFxRate(underlyingFx, ratesProvider);
CurrencyPair currencyPair = underlyingFx.CurrencyPair;
double forwardRate = forward.fxRate(currencyPair);
double strikeRate = option.Strike;
bool isCall = option.PutCall.Call;
SmileDeltaParameters smileAtTime = volatilities.Smile.smileForExpiry(timeToExpiry);
double[] strikes = smileAtTime.strike(forwardRate).toArray();
double[] vols = smileAtTime.Volatility.toArray();
double volAtm = vols[1];
double[] x = vannaVolgaWeights(forwardRate, strikeRate, timeToExpiry, volAtm, strikes);
double priceFwd = BlackFormulaRepository.price(forwardRate, strikeRate, timeToExpiry, volAtm, isCall);
double deltaFwd = BlackFormulaRepository.delta(forwardRate, strikeRate, timeToExpiry, volAtm, isCall);
for (int i = 0; i < 3; i += 2)
{
double priceFwdAtm = BlackFormulaRepository.price(forwardRate, strikes[i], timeToExpiry, volAtm, isCall);
double priceFwdSmile = BlackFormulaRepository.price(forwardRate, strikes[i], timeToExpiry, vols[i], isCall);
priceFwd += x[i] * (priceFwdSmile - priceFwdAtm);
double deltaFwdAtm = BlackFormulaRepository.delta(forwardRate, strikes[i], timeToExpiry, volAtm, isCall);
double deltaFwdSmile = BlackFormulaRepository.delta(forwardRate, strikes[i], timeToExpiry, vols[i], isCall);
deltaFwd += x[i] * (deltaFwdSmile - deltaFwdAtm);
}
double signedNotional = this.signedNotional(option);
PointSensitivityBuilder dfSensi = ratesProvider.discountFactors(ccyCounter).zeroRatePointSensitivity(underlyingFx.PaymentDate).multipliedBy(priceFwd * signedNotional);
PointSensitivityBuilder fwdSensi = fxPricer.forwardFxRatePointSensitivity(option.PutCall.Call ? underlyingFx : underlyingFx.inverse(), ratesProvider).multipliedBy(df * deltaFwd * signedNotional);
return(dfSensi.combinedWith(fwdSensi));
}
/// <summary>
/// Calculates the present value sensitivity of the product.
/// <para>
/// The present value sensitivity of the product is the sensitivity of present value to the underlying curves.
///
/// </para>
/// </summary>
/// <param name="cdsIndex"> the product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="referenceDate"> the reference date </param>
/// <param name="refData"> the reference data </param>
/// <returns> the present value sensitivity </returns>
public virtual PointSensitivityBuilder presentValueSensitivity(ResolvedCdsIndex cdsIndex, CreditRatesProvider ratesProvider, LocalDate referenceDate, ReferenceData refData)
{
if (isExpired(cdsIndex, ratesProvider))
{
return(PointSensitivityBuilder.none());
}
ResolvedCds cds = cdsIndex.toSingleNameCds();
LocalDate stepinDate = cds.StepinDateOffset.adjust(ratesProvider.ValuationDate, refData);
LocalDate effectiveStartDate = cds.calculateEffectiveStartDate(stepinDate);
double recoveryRate = underlyingPricer.recoveryRate(cds, ratesProvider);
Triple <CreditDiscountFactors, LegalEntitySurvivalProbabilities, double> rates = reduceDiscountFactors(cds, ratesProvider);
double signedNotional = cds.BuySell.normalize(cds.Notional);
PointSensitivityBuilder protectionLegSensi = underlyingPricer.protectionLegSensitivity(cds, rates.First, rates.Second, referenceDate, effectiveStartDate, recoveryRate);
protectionLegSensi = protectionLegSensi.multipliedBy(signedNotional * rates.Third);
PointSensitivityBuilder riskyAnnuitySensi = underlyingPricer.riskyAnnuitySensitivity(cds, rates.First, rates.Second, referenceDate, stepinDate, effectiveStartDate);
riskyAnnuitySensi = riskyAnnuitySensi.multipliedBy(-cds.FixedRate * signedNotional * rates.Third);
return(protectionLegSensi.combinedWith(riskyAnnuitySensi));
}
public virtual void pointAndParameterFx()
{
ImmutableRatesProvider test = ImmutableRatesProvider.builder(VAL_DATE).fxRateProvider(FX_MATRIX).discountCurve(GBP, DISCOUNT_CURVE_GBP).discountCurve(USD, DISCOUNT_CURVE_USD).build();
ImmutableRatesProvider test_gbp_up = ImmutableRatesProvider.builder(VAL_DATE).fxRateProvider(FX_MATRIX).discountCurve(GBP, DISCOUNT_CURVE_GBP_UP).discountCurve(USD, DISCOUNT_CURVE_USD).build();
ImmutableRatesProvider test_gbp_dw = ImmutableRatesProvider.builder(VAL_DATE).fxRateProvider(FX_MATRIX).discountCurve(GBP, DISCOUNT_CURVE_GBP_DOWN).discountCurve(USD, DISCOUNT_CURVE_USD).build();
ImmutableRatesProvider test_usd_up = ImmutableRatesProvider.builder(VAL_DATE).fxRateProvider(FX_MATRIX).discountCurve(GBP, DISCOUNT_CURVE_GBP).discountCurve(USD, DISCOUNT_CURVE_USD_UP).build();
ImmutableRatesProvider test_usd_dw = ImmutableRatesProvider.builder(VAL_DATE).fxRateProvider(FX_MATRIX).discountCurve(GBP, DISCOUNT_CURVE_GBP).discountCurve(USD, DISCOUNT_CURVE_USD_DOWN).build();
LocalDate matuirtyDate = GBP_USD_WM.calculateMaturityFromFixing(VAL_DATE, REF_DATA);
double maturityTime = DAY_COUNT.relativeYearFraction(VAL_DATE, matuirtyDate);
// GBP based
FxIndexObservation obs = FxIndexObservation.of(GBP_USD_WM, VAL_DATE, REF_DATA);
PointSensitivityBuilder sensiBuildCmpGBP = test.fxIndexRates(GBP_USD_WM).ratePointSensitivity(obs, GBP);
FxIndexSensitivity sensiBuildExpGBP = FxIndexSensitivity.of(obs, GBP, USD, 1.0);
assertTrue(sensiBuildCmpGBP.Equals(sensiBuildExpGBP));
double sense_gbp1 = 0.5 * (test_gbp_up.fxIndexRates(GBP_USD_WM).rate(obs, GBP) - test_gbp_dw.fxIndexRates(GBP_USD_WM).rate(obs, GBP)) / EPS_FD * (-maturityTime * GBP_DSC);
double sense_usd1 = 0.5 * (test_usd_up.fxIndexRates(GBP_USD_WM).rate(obs, GBP) - test_usd_dw.fxIndexRates(GBP_USD_WM).rate(obs, GBP)) / EPS_FD * (-maturityTime * USD_DSC);
PointSensitivityBuilder sensiBuildDecGBP = ZeroRateSensitivity.of(GBP, maturityTime, USD, sense_gbp1);
sensiBuildDecGBP = sensiBuildDecGBP.combinedWith(ZeroRateSensitivity.of(USD, maturityTime, USD, sense_usd1));
CurrencyParameterSensitivities paramSensiCmpGBP = test.parameterSensitivity(sensiBuildCmpGBP.build().normalized());
CurrencyParameterSensitivities paramSensiExpGBP = test.parameterSensitivity(sensiBuildDecGBP.build().normalized());
assertTrue(paramSensiCmpGBP.equalWithTolerance(paramSensiExpGBP, EPS_FD));
// USD based
PointSensitivityBuilder sensiBuildCmpUSD = test.fxIndexRates(GBP_USD_WM).ratePointSensitivity(obs, USD);
FxIndexSensitivity sensiBuildExpUSD = FxIndexSensitivity.of(obs, USD, GBP, 1.0);
assertTrue(sensiBuildCmpUSD.Equals(sensiBuildExpUSD));
double sense_gbp2 = 0.5 * (test_gbp_up.fxIndexRates(GBP_USD_WM).rate(obs, USD) - test_gbp_dw.fxIndexRates(GBP_USD_WM).rate(obs, USD)) / EPS_FD * (-maturityTime * GBP_DSC);
double sense_usd2 = 0.5 * (test_usd_up.fxIndexRates(GBP_USD_WM).rate(obs, USD) - test_usd_dw.fxIndexRates(GBP_USD_WM).rate(obs, USD)) / EPS_FD * (-maturityTime * USD_DSC);
PointSensitivityBuilder sensiBuildDecUSD = ZeroRateSensitivity.of(GBP, maturityTime, GBP, sense_gbp2);
sensiBuildDecUSD = sensiBuildDecUSD.combinedWith(ZeroRateSensitivity.of(USD, maturityTime, GBP, sense_usd2));
CurrencyParameterSensitivities paramSensiCmpUSD = test.parameterSensitivity(sensiBuildCmpUSD.build().normalized());
CurrencyParameterSensitivities paramSensiExpUSD = test.parameterSensitivity(sensiBuildDecUSD.build().normalized());
assertTrue(paramSensiCmpUSD.equalWithTolerance(paramSensiExpUSD, EPS_FD));
}
/// <summary>
/// Computes the present value sensitivity to the black volatilities used in the pricing.
/// <para>
/// The implied strikes and weights are fixed in this sensitivity computation.
///
/// </para>
/// </summary>
/// <param name="option"> the option product </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <param name="volatilities"> the Black volatility provider </param>
/// <returns> the present value sensitivity </returns>
public virtual PointSensitivityBuilder presentValueSensitivityModelParamsVolatility(ResolvedFxVanillaOption option, RatesProvider ratesProvider, BlackFxOptionSmileVolatilities volatilities)
{
validate(ratesProvider, volatilities);
double timeToExpiry = volatilities.relativeTime(option.Expiry);
if (timeToExpiry <= 0d)
{
return(PointSensitivityBuilder.none());
}
ResolvedFxSingle underlyingFx = option.Underlying;
Currency ccyCounter = option.CounterCurrency;
double df = ratesProvider.discountFactor(ccyCounter, underlyingFx.PaymentDate);
FxRate forward = fxPricer.forwardFxRate(underlyingFx, ratesProvider);
CurrencyPair currencyPair = underlyingFx.CurrencyPair;
double forwardRate = forward.fxRate(currencyPair);
double strikeRate = option.Strike;
SmileDeltaParameters smileAtTime = volatilities.Smile.smileForExpiry(timeToExpiry);
double[] strikes = smileAtTime.strike(forwardRate).toArray();
double[] vols = smileAtTime.Volatility.toArray();
double volAtm = vols[1];
double[] x = vannaVolgaWeights(forwardRate, strikeRate, timeToExpiry, volAtm, strikes);
double vegaAtm = BlackFormulaRepository.vega(forwardRate, strikeRate, timeToExpiry, volAtm);
double signedNotional = this.signedNotional(option);
PointSensitivityBuilder sensiSmile = PointSensitivityBuilder.none();
for (int i = 0; i < 3; i += 2)
{
double vegaFwdAtm = BlackFormulaRepository.vega(forwardRate, strikes[i], timeToExpiry, volAtm);
vegaAtm -= x[i] * vegaFwdAtm;
double vegaFwdSmile = BlackFormulaRepository.vega(forwardRate, strikes[i], timeToExpiry, vols[i]);
sensiSmile = sensiSmile.combinedWith(FxOptionSensitivity.of(volatilities.Name, currencyPair, timeToExpiry, strikes[i], forwardRate, ccyCounter, df * signedNotional * x[i] * vegaFwdSmile));
}
FxOptionSensitivity sensiAtm = FxOptionSensitivity.of(volatilities.Name, currencyPair, timeToExpiry, strikes[1], forwardRate, ccyCounter, df * signedNotional * vegaAtm);
return(sensiAtm.combinedWith(sensiSmile));
}
/// <summary>
/// Calculates the par rate curve sensitivity for a swap with a fixed leg.
/// <para>
/// The par rate is the common rate on all payments of the fixed leg for which the total swap present value is 0.
/// </para>
/// <para>
/// At least one leg must be a fixed leg. The par rate will be computed with respect to the first fixed leg.
/// All the payments in that leg should be fixed payments with a unique accrual period (no compounding) and no FX reset.
///
/// </para>
/// </summary>
/// <param name="swap"> the product </param>
/// <param name="provider"> the rates provider </param>
/// <returns> the par rate curve sensitivity of the swap product </returns>
public virtual PointSensitivityBuilder parRateSensitivity(ResolvedSwap swap, RatesProvider provider)
{
ResolvedSwapLeg fixedLeg = this.fixedLeg(swap);
Currency ccyFixedLeg = fixedLeg.Currency;
// other payments (not fixed leg coupons) converted in fixed leg currency
double otherLegsConvertedPv = 0.0;
foreach (ResolvedSwapLeg leg in swap.Legs)
{
if (leg != fixedLeg)
{
double pvLocal = legPricer.presentValueInternal(leg, provider);
otherLegsConvertedPv += (pvLocal * provider.fxRate(leg.Currency, ccyFixedLeg));
}
}
double fixedLegEventsPv = legPricer.presentValueEventsInternal(fixedLeg, provider);
double pvbpFixedLeg = legPricer.pvbp(fixedLeg, provider);
// Backward sweep
double otherLegsConvertedPvBar = -1.0d / pvbpFixedLeg;
double fixedLegEventsPvBar = -1.0d / pvbpFixedLeg;
double pvbpFixedLegBar = (otherLegsConvertedPv + fixedLegEventsPv) / (pvbpFixedLeg * pvbpFixedLeg);
PointSensitivityBuilder pvbpFixedLegDr = legPricer.pvbpSensitivity(fixedLeg, provider);
PointSensitivityBuilder fixedLegEventsPvDr = legPricer.presentValueSensitivityEventsInternal(fixedLeg, provider);
PointSensitivityBuilder otherLegsConvertedPvDr = PointSensitivityBuilder.none();
foreach (ResolvedSwapLeg leg in swap.Legs)
{
if (leg != fixedLeg)
{
PointSensitivityBuilder pvLegDr = legPricer.presentValueSensitivity(leg, provider).multipliedBy(provider.fxRate(leg.Currency, ccyFixedLeg));
otherLegsConvertedPvDr = otherLegsConvertedPvDr.combinedWith(pvLegDr);
}
}
otherLegsConvertedPvDr = otherLegsConvertedPvDr.withCurrency(ccyFixedLeg);
return(pvbpFixedLegDr.multipliedBy(pvbpFixedLegBar).combinedWith(fixedLegEventsPvDr.multipliedBy(fixedLegEventsPvBar)).combinedWith(otherLegsConvertedPvDr.multipliedBy(otherLegsConvertedPvBar)));
}
/// <summary>
/// Computes cash flow equivalent and sensitivity of Ibor leg.
/// <para>
/// The return type is a map of {@code NotionalExchange} and {@code PointSensitivityBuilder}.
///
/// </para>
/// </summary>
/// <param name="iborLeg"> the Ibor leg </param>
/// <param name="ratesProvider"> the rates provider </param>
/// <returns> the cash flow equivalent and sensitivity </returns>
public static ImmutableMap <Payment, PointSensitivityBuilder> cashFlowEquivalentAndSensitivityIborLeg(ResolvedSwapLeg iborLeg, RatesProvider ratesProvider)
{
ArgChecker.isTrue(iborLeg.Type.Equals(SwapLegType.IBOR), "Leg type should be IBOR");
ArgChecker.isTrue(iborLeg.PaymentEvents.Empty, "PaymentEvent should be empty");
IDictionary <Payment, PointSensitivityBuilder> res = new Dictionary <Payment, PointSensitivityBuilder>();
foreach (SwapPaymentPeriod paymentPeriod in iborLeg.PaymentPeriods)
{
ArgChecker.isTrue(paymentPeriod is RatePaymentPeriod, "rate payment should be RatePaymentPeriod");
RatePaymentPeriod ratePaymentPeriod = (RatePaymentPeriod)paymentPeriod;
ArgChecker.isTrue(ratePaymentPeriod.AccrualPeriods.size() == 1, "rate payment should not be compounding");
RateAccrualPeriod rateAccrualPeriod = ratePaymentPeriod.AccrualPeriods.get(0);
CurrencyAmount notional = ratePaymentPeriod.NotionalAmount;
LocalDate paymentDate = ratePaymentPeriod.PaymentDate;
IborIndexObservation obs = ((IborRateComputation)rateAccrualPeriod.RateComputation).Observation;
IborIndex index = obs.Index;
LocalDate fixingStartDate = obs.EffectiveDate;
double fixingYearFraction = obs.YearFraction;
double factorIndex = (1d + fixingYearFraction * ratesProvider.iborIndexRates(index).rate(obs));
double dfPayment = ratesProvider.discountFactor(paymentPeriod.Currency, paymentPeriod.PaymentDate);
double dfStart = ratesProvider.discountFactor(paymentPeriod.Currency, fixingStartDate);
double beta = factorIndex * dfPayment / dfStart;
double ycRatio = rateAccrualPeriod.YearFraction / fixingYearFraction;
Payment payStart = Payment.of(notional.multipliedBy(beta * ycRatio), fixingStartDate);
Payment payEnd = Payment.of(notional.multipliedBy(-ycRatio), paymentDate);
double factor = ycRatio * notional.Amount / dfStart;
PointSensitivityBuilder factorIndexSensi = ratesProvider.iborIndexRates(index).ratePointSensitivity(obs).multipliedBy(fixingYearFraction * dfPayment * factor);
PointSensitivityBuilder dfPaymentSensitivity = ratesProvider.discountFactors(paymentPeriod.Currency).zeroRatePointSensitivity(paymentPeriod.PaymentDate).multipliedBy(factorIndex * factor);
PointSensitivityBuilder dfStartSensitivity = ratesProvider.discountFactors(paymentPeriod.Currency).zeroRatePointSensitivity(fixingStartDate).multipliedBy(-factorIndex * dfPayment * factor / dfStart);
res[payStart] = factorIndexSensi.combinedWith(dfPaymentSensitivity).combinedWith(dfStartSensitivity);
res[payEnd] = PointSensitivityBuilder.none();
}
return(ImmutableMap.copyOf(res));
}
private Pair <double, PointSensitivityBuilder> singlePeriodAccrualOnDefaultSensitivity(CreditCouponPaymentPeriod coupon, LocalDate effectiveStartDate, DoubleArray integrationSchedule, CreditDiscountFactors discountFactors, LegalEntitySurvivalProbabilities survivalProbabilities)
{
LocalDate start = coupon.EffectiveStartDate.isBefore(effectiveStartDate) ? effectiveStartDate : coupon.EffectiveStartDate;
if (!start.isBefore(coupon.EffectiveEndDate))
{
return(Pair.of(0d, PointSensitivityBuilder.none())); //this coupon has already expired
}
DoubleArray knots = DoublesScheduleGenerator.truncateSetInclusive(discountFactors.relativeYearFraction(start), discountFactors.relativeYearFraction(coupon.EffectiveEndDate), integrationSchedule);
// pv
double pv = 0d;
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final int nItems = knots.size();
int nItems = knots.size();
double[] dhrtBar = new double[nItems - 1];
double[] dhtBar = new double[nItems - 1];
double[] bBar = new double[nItems];
double[] p = new double[nItems];
double[] q = new double[nItems];
double t = knots.get(0);
double ht0 = survivalProbabilities.zeroRate(t) * t;
double rt0 = discountFactors.zeroRate(t) * t;
q[0] = Math.Exp(-ht0);
p[0] = Math.Exp(-rt0);
double b0 = q[0] * p[0];
double effStart = discountFactors.relativeYearFraction(coupon.EffectiveStartDate);
double t0 = t - effStart + omega;
for (int i = 1; i < nItems; ++i)
{
t = knots.get(i);
double ht1 = survivalProbabilities.zeroRate(t) * t;
double rt1 = discountFactors.zeroRate(t) * t;
q[i] = Math.Exp(-ht1);
p[i] = Math.Exp(-rt1);
double b1 = q[i] * p[i];
double dt = knots.get(i) - knots.get(i - 1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
double tPv;
if (formula == AccrualOnDefaultFormula.MARKIT_FIX)
{
if (Math.Abs(dhrt) < SMALL)
{
double eps = epsilonP(-dhrt);
tPv = dht * dt * b0 * eps;
dhtBar[i - 1] = dt * b0 * eps;
dhrtBar[i - 1] = -dht *dt *b0 *epsilonPP(-dhrt);
bBar[i - 1] += dht * eps;
}
else
{
tPv = dht * dt / dhrt * ((b0 - b1) / dhrt - b1);
dhtBar[i - 1] = dt / dhrt * ((b0 - b1) / dhrt - b1);
dhrtBar[i - 1] = dht * dt / (dhrt * dhrt) * (b1 - 2d * (b0 - b1) / dhrt);
bBar[i - 1] += dht * dt / (dhrt * dhrt);
bBar[i] += -dht * dt / dhrt * (1d + 1d / dhrt);
}
}
else
{
double t1 = t - effStart + omega;
if (Math.Abs(dhrt) < SMALL)
{
double eps = epsilon(-dhrt);
double epsp = epsilonP(-dhrt);
tPv = dht * b0 * (t0 * eps + dt * epsp);
dhtBar[i - 1] = b0 * (t0 * eps + dt * epsp);
dhrtBar[i - 1] = -dht * b0 * (t0 * epsp + dt * epsilonPP(-dhrt));
bBar[i - 1] += dht * (t0 * eps + dt * epsp);
}
else
{
tPv = dht / dhrt * (t0 * b0 - t1 * b1 + dt / dhrt * (b0 - b1));
dhtBar[i - 1] = (t0 * b0 - t1 * b1 + dt / dhrt * (b0 - b1)) / dhrt;
dhrtBar[i - 1] = dht / (dhrt * dhrt) * (-2d * dt / dhrt * (b0 - b1) - t0 * b0 + t1 * b1);
bBar[i - 1] += dht / dhrt * (t0 + dt / dhrt);
bBar[i] += dht / dhrt * (-t1 - dt / dhrt);
}
t0 = t1;
}
pv += tPv;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
double yfRatio = coupon.YearFraction / discountFactors.DayCount.relativeYearFraction(coupon.StartDate, coupon.EndDate);
// pv sensitivity
PointSensitivityBuilder qSensiFirst = survivalProbabilities.zeroRatePointSensitivity(knots.get(0)).multipliedBy(yfRatio * ((dhrtBar[0] + dhtBar[0]) / q[0] + bBar[0] * p[0]));
PointSensitivityBuilder pSensiFirst = discountFactors.zeroRatePointSensitivity(knots.get(0)).multipliedBy(yfRatio * (dhrtBar[0] / p[0] + bBar[0] * q[0]));
PointSensitivityBuilder pvSensi = pSensiFirst.combinedWith(qSensiFirst);
for (int i = 1; i < nItems - 1; ++i)
{
PointSensitivityBuilder qSensi = survivalProbabilities.zeroRatePointSensitivity(knots.get(i)).multipliedBy(yfRatio * (-(dhrtBar[i - 1] + dhtBar[i - 1]) / q[i] + (dhrtBar[i] + dhtBar[i]) / q[i] + bBar[i] * p[i]));
PointSensitivityBuilder pSensi = discountFactors.zeroRatePointSensitivity(knots.get(i)).multipliedBy(yfRatio * (-dhrtBar[i - 1] / p[i] + dhrtBar[i] / p[i] + bBar[i] * q[i]));
pvSensi = pvSensi.combinedWith(pSensi).combinedWith(qSensi);
}
if (nItems > 1)
{
PointSensitivityBuilder qSensiLast = survivalProbabilities.zeroRatePointSensitivity(knots.get(nItems - 1)).multipliedBy(yfRatio * (-(dhrtBar[nItems - 2] + dhtBar[nItems - 2]) / q[nItems - 1] + bBar[nItems - 1] * p[nItems - 1]));
PointSensitivityBuilder pSensiLast = discountFactors.zeroRatePointSensitivity(knots.get(nItems - 1)).multipliedBy(yfRatio * (-dhrtBar[nItems - 2] / p[nItems - 1] + bBar[nItems - 1] * q[nItems - 1]));
pvSensi = pvSensi.combinedWith(pSensiLast).combinedWith(qSensiLast);
}
return(Pair.of(yfRatio * pv, pvSensi));
}
//-------------------------------------------------------------------------
/// <summary>
/// Computes the present value curve sensitivity by replication in SABR framework with extrapolation on the right.
/// </summary>
/// <param name="cmsPeriod"> the CMS </param>
/// <param name="provider"> the rates provider </param>
/// <param name="swaptionVolatilities"> the swaption volatilities </param>
/// <returns> the present value sensitivity </returns>
public PointSensitivityBuilder presentValueSensitivityRates(CmsPeriod cmsPeriod, RatesProvider provider, SabrSwaptionVolatilities swaptionVolatilities)
{
Currency ccy = cmsPeriod.Currency;
if (provider.ValuationDate.isAfter(cmsPeriod.PaymentDate))
{
return(PointSensitivityBuilder.none());
}
SwapIndex index = cmsPeriod.Index;
ResolvedSwap swap = cmsPeriod.UnderlyingSwap;
double dfPayment = provider.discountFactor(ccy, cmsPeriod.PaymentDate);
ZonedDateTime valuationDate = swaptionVolatilities.ValuationDateTime;
LocalDate fixingDate = cmsPeriod.FixingDate;
double expiryTime = swaptionVolatilities.relativeTime(fixingDate.atTime(index.FixingTime).atZone(index.FixingZone));
double tenor = swaptionVolatilities.tenor(swap.StartDate, swap.EndDate);
double shift = swaptionVolatilities.shift(expiryTime, tenor);
double strikeCpn = cmsPeriod.CmsPeriodType.Equals(CmsPeriodType.COUPON) ? -shift : cmsPeriod.Strike;
if (!fixingDate.isAfter(valuationDate.toLocalDate()))
{
double?fixedRate = provider.timeSeries(cmsPeriod.Index).get(fixingDate);
if (fixedRate.HasValue)
{
double payoff = payOff(cmsPeriod.CmsPeriodType, strikeCpn, fixedRate.Value);
return(provider.discountFactors(ccy).zeroRatePointSensitivity(cmsPeriod.PaymentDate).multipliedBy(payoff * cmsPeriod.Notional * cmsPeriod.YearFraction));
}
else if (fixingDate.isBefore(valuationDate.toLocalDate()))
{
throw new System.ArgumentException(Messages.format("Unable to get fixing for {} on date {}, no time-series supplied", cmsPeriod.Index, fixingDate));
}
}
double forward = swapPricer.parRate(swap, provider);
double eta = index.Template.Convention.FixedLeg.DayCount.relativeYearFraction(cmsPeriod.PaymentDate, swap.StartDate);
CmsDeltaIntegrantProvider intProv = new CmsDeltaIntegrantProvider(this, cmsPeriod, swap, swaptionVolatilities, forward, strikeCpn, expiryTime, tenor, cutOffStrike, eta);
RungeKuttaIntegrator1D integrator = new RungeKuttaIntegrator1D(ABS_TOL, REL_TOL, NUM_ITER);
double[] bs = intProv.bsbsp(strikeCpn);
double[] n = intProv.Nnp;
double strikePartPrice = intProv.k(strikeCpn) * n[0] * bs[0];
double integralPartPrice = 0d;
double integralPart = 0d;
System.Func <double, double> integrant = intProv.integrant();
System.Func <double, double> integrantDelta = intProv.integrantDelta();
try
{
if (intProv.PutCall.Call)
{
integralPartPrice = integrateCall(integrator, integrant, swaptionVolatilities, forward, strikeCpn, expiryTime, tenor);
integralPart = dfPayment * integrateCall(integrator, integrantDelta, swaptionVolatilities, forward, strikeCpn, expiryTime, tenor);
}
else
{
integralPartPrice = -integrator.integrate(integrant, -shift + ZERO_SHIFT, strikeCpn).Value;
integralPart = -dfPayment *integrator.integrate(integrantDelta, -shift, strikeCpn);
}
}
catch (Exception e)
{
throw new MathException(e);
}
double deltaPD = strikePartPrice + integralPartPrice;
if (cmsPeriod.CmsPeriodType.Equals(CmsPeriodType.COUPON))
{
deltaPD -= shift;
}
deltaPD *= cmsPeriod.Notional * cmsPeriod.YearFraction;
double strikePart = dfPayment * intProv.k(strikeCpn) * (n[1] * bs[0] + n[0] * bs[1]);
double deltaFwd = (strikePart + integralPart) * cmsPeriod.Notional * cmsPeriod.YearFraction;
PointSensitivityBuilder sensiFwd = swapPricer.parRateSensitivity(swap, provider).multipliedBy(deltaFwd);
PointSensitivityBuilder sensiDf = provider.discountFactors(ccy).zeroRatePointSensitivity(cmsPeriod.PaymentDate).multipliedBy(deltaPD);
return(sensiFwd.combinedWith(sensiDf));
}
//-------------------------------------------------------------------------
internal virtual PointSensitivityBuilder protectionLegSensitivity(ResolvedCds cds, CreditDiscountFactors discountFactors, LegalEntitySurvivalProbabilities survivalProbabilities, LocalDate referenceDate, LocalDate effectiveStartDate, double recoveryRate)
{
DoubleArray integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(discountFactors.relativeYearFraction(effectiveStartDate), discountFactors.relativeYearFraction(cds.ProtectionEndDate), discountFactors.ParameterKeys, survivalProbabilities.ParameterKeys);
int n = integrationSchedule.size();
double[] dht = new double[n - 1];
double[] drt = new double[n - 1];
double[] dhrt = new double[n - 1];
double[] p = new double[n];
double[] q = new double[n];
// pv
double pv = 0d;
double ht0 = survivalProbabilities.zeroRate(integrationSchedule.get(0)) * integrationSchedule.get(0);
double rt0 = discountFactors.zeroRate(integrationSchedule.get(0)) * integrationSchedule.get(0);
p[0] = Math.Exp(-rt0);
q[0] = Math.Exp(-ht0);
double b0 = p[0] * q[0];
for (int i = 1; i < n; ++i)
{
double ht1 = survivalProbabilities.zeroRate(integrationSchedule.get(i)) * integrationSchedule.get(i);
double rt1 = discountFactors.zeroRate(integrationSchedule.get(i)) * integrationSchedule.get(i);
p[i] = Math.Exp(-rt1);
q[i] = Math.Exp(-ht1);
double b1 = p[i] * q[i];
dht[i - 1] = ht1 - ht0;
drt[i - 1] = rt1 - rt0;
dhrt[i - 1] = dht[i - 1] + drt[i - 1];
double dPv = 0d;
if (Math.Abs(dhrt[i - 1]) < SMALL)
{
double eps = epsilon(-dhrt[i - 1]);
dPv = dht[i - 1] * b0 * eps;
}
else
{
dPv = (b0 - b1) * dht[i - 1] / dhrt[i - 1];
}
pv += dPv;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
double df = discountFactors.discountFactor(referenceDate);
// pv sensitivity
double factor = (1d - recoveryRate) / df;
double eps0 = computeExtendedEpsilon(-dhrt[0], p[1], q[1], p[0], q[0]);
PointSensitivityBuilder pvSensi = discountFactors.zeroRatePointSensitivity(integrationSchedule.get(0)).multipliedBy(-dht[0] * q[0] * eps0 * factor);
pvSensi = pvSensi.combinedWith(survivalProbabilities.zeroRatePointSensitivity(integrationSchedule.get(0)).multipliedBy(factor * (drt[0] * p[0] * eps0 + p[0])));
for (int i = 1; i < n - 1; ++i)
{
double epsp = computeExtendedEpsilon(-dhrt[i], p[i + 1], q[i + 1], p[i], q[i]);
double epsm = computeExtendedEpsilon(dhrt[i - 1], p[i - 1], q[i - 1], p[i], q[i]);
PointSensitivityBuilder pSensi = discountFactors.zeroRatePointSensitivity(integrationSchedule.get(i)).multipliedBy(factor * (-dht[i] * q[i] * epsp - dht[i - 1] * q[i] * epsm));
PointSensitivityBuilder qSensi = survivalProbabilities.zeroRatePointSensitivity(integrationSchedule.get(i)).multipliedBy(factor * (drt[i - 1] * p[i] * epsm + drt[i] * p[i] * epsp));
pvSensi = pvSensi.combinedWith(pSensi).combinedWith(qSensi);
}
if (n > 1)
{
double epsLast = computeExtendedEpsilon(dhrt[n - 2], p[n - 2], q[n - 2], p[n - 1], q[n - 1]);
pvSensi = pvSensi.combinedWith(discountFactors.zeroRatePointSensitivity(integrationSchedule.get(n - 1)).multipliedBy(-dht[n - 2] * q[n - 1] * epsLast * factor));
pvSensi = pvSensi.combinedWith(survivalProbabilities.zeroRatePointSensitivity(integrationSchedule.get(n - 1)).multipliedBy(factor * (drt[n - 2] * p[n - 1] * epsLast - p[n - 1])));
}
PointSensitivityBuilder dfSensi = discountFactors.zeroRatePointSensitivity(referenceDate).multipliedBy(-pv * factor / df);
return(dfSensi.combinedWith(pvSensi));
}
