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Pricers for overnight in-arrears cap/floor. (#2410)
* Pricer for overnight in-arrears cap/floor. Present value in pricer SABR and volatility based. * PR comments Co-authored-by: Guillaume Santoro <31656059+santorog@users.noreply.github.com>
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...om/opengamma/strata/pricer/capfloor/SabrOvernightInArrearsCapletFloorletPeriodPricer.java
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| /* | ||
| * Copyright (C) 2022 - present by OpenGamma Inc. and the OpenGamma group of companies | ||
| * | ||
| * Please see distribution for license. | ||
| */ | ||
| package com.opengamma.strata.pricer.capfloor; | ||
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| import static com.opengamma.strata.market.model.SabrParameterType.ALPHA; | ||
| import static com.opengamma.strata.market.model.SabrParameterType.BETA; | ||
| import static com.opengamma.strata.market.model.SabrParameterType.NU; | ||
| import static com.opengamma.strata.market.model.SabrParameterType.RHO; | ||
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| import java.time.LocalDate; | ||
| import java.time.ZoneOffset; | ||
| import java.util.List; | ||
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| import com.opengamma.strata.basics.currency.Currency; | ||
| import com.opengamma.strata.basics.currency.CurrencyAmount; | ||
| import com.opengamma.strata.basics.value.ValueDerivatives; | ||
| import com.opengamma.strata.collect.array.DoubleArray; | ||
| import com.opengamma.strata.market.sensitivity.PointSensitivityBuilder; | ||
| import com.opengamma.strata.pricer.ZeroRateSensitivity; | ||
| import com.opengamma.strata.pricer.impl.option.BlackFormulaRepository; | ||
| import com.opengamma.strata.pricer.impl.rate.ForwardOvernightCompoundedRateComputationFn; | ||
| import com.opengamma.strata.pricer.impl.volatility.smile.SabrFormulaData; | ||
| import com.opengamma.strata.pricer.impl.volatility.smile.SabrInArrearsVolatilityFunction; | ||
| import com.opengamma.strata.pricer.rate.RatesProvider; | ||
| import com.opengamma.strata.product.capfloor.OvernightInArrearsCapletFloorletPeriod; | ||
| import com.opengamma.strata.product.common.PutCall; | ||
| import com.opengamma.strata.product.rate.OvernightCompoundedRateComputation; | ||
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| /** | ||
| * Pricer for in-arrears caplets and floorlets (Asian style options) in the SABR with effective parameters approach. | ||
| */ | ||
| public class SabrOvernightInArrearsCapletFloorletPeriodPricer { | ||
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| /** | ||
| * The default function for Asian in-arrears effective parameters. | ||
| */ | ||
| private final SabrInArrearsVolatilityFunction sabrInArrearsFunction; | ||
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| /** | ||
| * Default implementation. | ||
| */ | ||
| public static final SabrOvernightInArrearsCapletFloorletPeriodPricer DEFAULT = | ||
| new SabrOvernightInArrearsCapletFloorletPeriodPricer(SabrInArrearsVolatilityFunction.DEFAULT); | ||
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| /** | ||
| * Creates an instance. | ||
| * | ||
| * @param sabrInarrearsFunction the function for Asian in-arrears effective parameters | ||
| */ | ||
| private SabrOvernightInArrearsCapletFloorletPeriodPricer(SabrInArrearsVolatilityFunction sabrInarrearsFunction) { | ||
| this.sabrInArrearsFunction = sabrInarrearsFunction; | ||
| } | ||
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|
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| /** | ||
| * Creates an instance. | ||
| * | ||
| * @param sabrInarrearsFunction the function for Asian in-arrears effective parameters | ||
| * @return the instance | ||
| */ | ||
| public static SabrOvernightInArrearsCapletFloorletPeriodPricer | ||
| of(SabrInArrearsVolatilityFunction sabrInarrearsFunction) { | ||
| return new SabrOvernightInArrearsCapletFloorletPeriodPricer(sabrInarrearsFunction); | ||
| } | ||
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| /** | ||
| * The function to compute overnight rates, including if necessary the past composition from time series. | ||
| */ | ||
| private static final ForwardOvernightCompoundedRateComputationFn ON_FUNCT = | ||
| ForwardOvernightCompoundedRateComputationFn.DEFAULT; | ||
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||
| /** | ||
| * Computes the present value in the SABR model with effective parameters. | ||
| * | ||
| * @param period the caplet/floorlet period | ||
| * @param ratesProvider the rates provider | ||
| * @param sabrVolatilities the SABR volatilities | ||
| * @return the present value | ||
| */ | ||
| public CurrencyAmount presentValue( | ||
| OvernightInArrearsCapletFloorletPeriod period, | ||
| RatesProvider ratesProvider, | ||
| SabrParametersIborCapletFloorletVolatilities sabrVolatilities) { | ||
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| Currency currency = period.getCurrency(); | ||
| if (ratesProvider.getValuationDate().isAfter(period.getPaymentDate())) { | ||
| return CurrencyAmount.of(currency, 0d); | ||
| } | ||
| OvernightCompoundedRateComputation onComputation = period.getOvernightRate(); | ||
| LocalDate startDate = onComputation.getStartDate(); | ||
| LocalDate endDate = onComputation.getEndDate(); | ||
| double startTime = sabrVolatilities.relativeTime(startDate.atStartOfDay(ZoneOffset.UTC)); // The ON rates don't have an exact fixing time | ||
| double endTime = sabrVolatilities.relativeTime(endDate.atStartOfDay(ZoneOffset.UTC)); | ||
| double df = ratesProvider.discountFactor(currency, period.getPaymentDate()); | ||
| PutCall putCall = period.getPutCall(); | ||
| double strike = period.getStrike(); | ||
| double forward = ON_FUNCT | ||
| .rate(onComputation, onComputation.getStartDate(), onComputation.getEndDate(), ratesProvider); | ||
| if (!ratesProvider.getValuationDate().isBefore(period.getEndDate())) { // Between end compounding and payment date | ||
| double dfPayment = ratesProvider.discountFactor(currency, period.getPaymentDate()); | ||
| return period.payoff(forward).multipliedBy(dfPayment); | ||
| } | ||
| double alpha = sabrVolatilities.alpha(startTime); // parameters at start of composition period, for coherence with term rate caplets | ||
| double beta = sabrVolatilities.beta(startTime); | ||
| double rho = sabrVolatilities.rho(startTime); | ||
| double nu = sabrVolatilities.nu(startTime); | ||
| double shift = sabrVolatilities.shift(startTime); | ||
| SabrFormulaData sabr = SabrFormulaData.of(alpha, beta, rho, nu); | ||
| SabrFormulaData sabrAdjusted = sabrInArrearsFunction.effectiveSabr(sabr, startTime, endTime); | ||
| double volatility = sabrVolatilities.getParameters().getSabrVolatilityFormula() | ||
| .volatility(forward + shift, strike + shift, endTime, | ||
| sabrAdjusted.getAlpha(), sabrAdjusted.getBeta(), sabrAdjusted.getRho(), sabrAdjusted.getNu()); | ||
| double price = df * period.getYearFraction() * | ||
| BlackFormulaRepository.price(forward + shift, strike + shift, endTime, volatility, putCall.isCall()); | ||
| return CurrencyAmount.of(currency, price * period.getNotional()); | ||
| } | ||
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| /** | ||
| * Computes the present value sensitivity to the rate with "sticky SABR model parameters". | ||
| * | ||
| * @param period the caplet/floorlet period | ||
| * @param ratesProvider the rates provider | ||
| * @param sabrVolatilities the SABR volatilities | ||
| * @return the present value rate sensitivity | ||
| */ | ||
| public PointSensitivityBuilder presentValueSensitivityRatesStickyModel( | ||
| OvernightInArrearsCapletFloorletPeriod period, | ||
| RatesProvider ratesProvider, | ||
| SabrParametersIborCapletFloorletVolatilities sabrVolatilities) { | ||
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| Currency currency = period.getCurrency(); | ||
| if (ratesProvider.getValuationDate().isAfter(period.getPaymentDate())) { | ||
| return PointSensitivityBuilder.none(); | ||
| } | ||
| OvernightCompoundedRateComputation onComputation = period.getOvernightRate(); | ||
| LocalDate startDate = onComputation.getStartDate(); | ||
| LocalDate endDate = onComputation.getEndDate(); | ||
| double startTime = sabrVolatilities.relativeTime(startDate.atStartOfDay(ZoneOffset.UTC)); // The ON rates don't have an exact fixing time | ||
| double endTime = sabrVolatilities.relativeTime(endDate.atStartOfDay(ZoneOffset.UTC)); | ||
| double df = ratesProvider.discountFactor(currency, period.getPaymentDate()); | ||
| PutCall putCall = period.getPutCall(); | ||
| double strike = period.getStrike(); | ||
| double forward = ON_FUNCT | ||
| .rate(onComputation, onComputation.getStartDate(), onComputation.getEndDate(), ratesProvider); | ||
| if (!ratesProvider.getValuationDate().isBefore(period.getEndDate())) { // Between end compounding and payment date | ||
| double pvForward = period.payoff(forward).getAmount(); | ||
| // Backward sweep | ||
| double dfPaymentBar = pvForward; | ||
| ZeroRateSensitivity ddfPaymentdr = ratesProvider | ||
| .discountFactors(currency).zeroRatePointSensitivity(period.getPaymentDate()); | ||
| return ddfPaymentdr.multipliedBy(dfPaymentBar); | ||
| } | ||
| double alpha = sabrVolatilities.alpha(startTime); | ||
| double beta = sabrVolatilities.beta(startTime); | ||
| double rho = sabrVolatilities.rho(startTime); | ||
| double nu = sabrVolatilities.nu(startTime); | ||
| double shift = sabrVolatilities.shift(startTime); | ||
| SabrFormulaData sabr = SabrFormulaData.of(alpha, beta, rho, nu); | ||
| SabrFormulaData sabrAdjusted = sabrInArrearsFunction.effectiveSabr(sabr, startTime, endTime); | ||
| ValueDerivatives volatility = sabrVolatilities.getParameters().getSabrVolatilityFormula() | ||
| .volatilityAdjoint(forward + shift, strike + shift, endTime, | ||
| sabrAdjusted.getAlpha(), sabrAdjusted.getBeta(), sabrAdjusted.getRho(), sabrAdjusted.getNu()); | ||
| ValueDerivatives price = BlackFormulaRepository | ||
| .priceAdjoint(forward + shift, strike + shift, endTime, volatility.getValue(), putCall.isCall()); | ||
| double pv = price.getValue() * df * period.getYearFraction() * period.getNotional(); | ||
| // Backward sweep | ||
| double pvBar = 1.0; | ||
| double priceBar = df * period.getYearFraction() * period.getNotional() * pvBar; | ||
| double dfBar = pv / df * pvBar; | ||
| double forwardBar = price.getDerivative(0) * priceBar; | ||
| double volatilityBar = price.getDerivative(3) * priceBar; | ||
| forwardBar += volatility.getDerivative(0) * volatilityBar; | ||
| PointSensitivityBuilder dforwarddr = ON_FUNCT | ||
| .rateSensitivity(onComputation, onComputation.getStartDate(), onComputation.getEndDate(), ratesProvider); | ||
| ZeroRateSensitivity ddfdr = ratesProvider | ||
| .discountFactors(currency).zeroRatePointSensitivity(period.getPaymentDate()); | ||
| return ddfdr.multipliedBy(dfBar).combinedWith(dforwarddr.multipliedBy(forwardBar)); | ||
| } | ||
|
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| /** | ||
| * Computes the present value sensitivity to the SABR model parameters. | ||
| * | ||
| * @param period the caplet/floorlet period | ||
| * @param ratesProvider the rates provider | ||
| * @param sabrVolatilities the SABR volatilities | ||
| * @return the present value model parameters sensitivity | ||
| */ | ||
| public PointSensitivityBuilder presentValueSensitivityModelParamsSabr( | ||
| OvernightInArrearsCapletFloorletPeriod period, | ||
| RatesProvider ratesProvider, | ||
| SabrParametersIborCapletFloorletVolatilities sabrVolatilities) { | ||
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| Currency currency = period.getCurrency(); | ||
| if (!ratesProvider.getValuationDate().isBefore(period.getEndDate())) { | ||
| return PointSensitivityBuilder.none(); | ||
| } | ||
| OvernightCompoundedRateComputation onComputation = period.getOvernightRate(); | ||
| LocalDate startDate = onComputation.getStartDate(); | ||
| LocalDate endDate = onComputation.getEndDate(); | ||
| double startTime = sabrVolatilities.relativeTime(startDate.atStartOfDay(ZoneOffset.UTC)); | ||
| double endTime = sabrVolatilities.relativeTime(endDate.atStartOfDay(ZoneOffset.UTC)); | ||
| double df = ratesProvider.discountFactor(currency, period.getPaymentDate()); | ||
| PutCall putCall = period.getPutCall(); | ||
| double strike = period.getStrike(); | ||
| double forward = ON_FUNCT | ||
| .rate(onComputation, onComputation.getStartDate(), onComputation.getEndDate(), ratesProvider); | ||
| double alpha = sabrVolatilities.alpha(startTime); | ||
| double beta = sabrVolatilities.beta(startTime); | ||
| double rho = sabrVolatilities.rho(startTime); | ||
| double nu = sabrVolatilities.nu(startTime); | ||
| double shift = sabrVolatilities.shift(startTime); | ||
| SabrFormulaData sabr = SabrFormulaData.of(alpha, beta, rho, nu); | ||
| List<ValueDerivatives> sabrAdjusted = sabrInArrearsFunction.effectiveSabrAd(sabr, startTime, endTime); | ||
| ValueDerivatives volatility = sabrVolatilities.getParameters().getSabrVolatilityFormula() | ||
| .volatilityAdjoint(forward + shift, strike + shift, endTime, | ||
| sabrAdjusted.get(0).getValue(), sabrAdjusted.get(1).getValue(), | ||
| sabrAdjusted.get(2).getValue(), sabrAdjusted.get(3).getValue()); | ||
| ValueDerivatives price = BlackFormulaRepository | ||
| .priceAdjoint(forward + shift, strike + shift, endTime, volatility.getValue(), putCall.isCall()); | ||
| // Backward sweep | ||
| double pvBar = 1.0; | ||
| double priceBar = df * period.getYearFraction() * period.getNotional() * pvBar; | ||
| double volatilityBar = price.getDerivative(3) * priceBar; | ||
| double alphaHatBar = volatility.getDerivative(2) * volatilityBar; | ||
| double betaHatBar = volatility.getDerivative(3) * volatilityBar; | ||
| double rhoHatBar = volatility.getDerivative(4) * volatilityBar; | ||
| double nuHatBar = volatility.getDerivative(5) * volatilityBar; | ||
| DoubleArray paramHat = sabrAdjusted.get(0).getDerivatives().multipliedBy(alphaHatBar); | ||
| paramHat = paramHat.plus(sabrAdjusted.get(1).getDerivatives().multipliedBy(betaHatBar)); | ||
| paramHat = paramHat.plus(sabrAdjusted.get(2).getDerivatives().multipliedBy(rhoHatBar)); | ||
| paramHat = paramHat.plus(sabrAdjusted.get(3).getDerivatives().multipliedBy(nuHatBar)); | ||
| IborCapletFloorletVolatilitiesName name = sabrVolatilities.getName(); | ||
| return PointSensitivityBuilder.of( | ||
| IborCapletFloorletSabrSensitivity.of(name, startTime, ALPHA, currency, paramHat.get(0)), | ||
| IborCapletFloorletSabrSensitivity.of(name, startTime, BETA, currency, paramHat.get(1)), | ||
| IborCapletFloorletSabrSensitivity.of(name, startTime, RHO, currency, paramHat.get(2)), | ||
| IborCapletFloorletSabrSensitivity.of(name, startTime, NU, currency, paramHat.get(3))); | ||
| } | ||
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| } |
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