com.opengamma.strata.pricer.capfloor.SabrOvernightInArrearsCapletFloorletPeriodPricer Maven / Gradle / Ivy
/*
* Copyright (C) 2022 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.strata.pricer.capfloor;
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;
import java.time.LocalDate;
import java.time.ZoneOffset;
import java.util.List;
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.ArgChecker;
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;
/**
* Pricer for in-arrears caplets and floorlets (Asian style options) in the SABR with effective parameters approach.
*/
public class SabrOvernightInArrearsCapletFloorletPeriodPricer {
/**
* The default function for Asian in-arrears effective parameters.
*/
private final SabrInArrearsVolatilityFunction sabrInArrearsFunction;
/**
* Default implementation.
*/
public static final SabrOvernightInArrearsCapletFloorletPeriodPricer DEFAULT =
new SabrOvernightInArrearsCapletFloorletPeriodPricer(SabrInArrearsVolatilityFunction.DEFAULT);
/**
* Creates an instance.
*
* @param sabrInarrearsFunction the function for Asian in-arrears effective parameters
*/
private SabrOvernightInArrearsCapletFloorletPeriodPricer(SabrInArrearsVolatilityFunction sabrInarrearsFunction) {
this.sabrInArrearsFunction = sabrInarrearsFunction;
}
/**
* 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);
}
/**
* The function to compute overnight rates, including if necessary the past composition from time series.
*/
private static final ForwardOvernightCompoundedRateComputationFn ON_FUNCT =
ForwardOvernightCompoundedRateComputationFn.DEFAULT;
/**
* 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) {
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)); // 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());
}
/**
* 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) {
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)); // 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));
}
/**
* 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) {
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 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)));
}
//-------------------------------------------------------------------------
/**
* Computes the implied volatility of the caplet/floorlet.
*
* @param period the caplet/floorlet period
* @param ratesProvider the rates provider
* @param sabrVolatilities the SABR volatilities
* @return the implied volatility
*/
public double impliedVolatility(
OvernightInArrearsCapletFloorletPeriod period,
RatesProvider ratesProvider,
SabrParametersIborCapletFloorletVolatilities sabrVolatilities) {
OvernightCompoundedRateComputation onComputation = period.getOvernightRate();
LocalDate startDate = onComputation.getStartDate();
LocalDate endDate = onComputation.getEndDate();
double startTime = sabrVolatilities.relativeTime(startDate.atStartOfDay(ZoneOffset.UTC)); // ON rates don't have an exact fixing time
double endTime = sabrVolatilities.relativeTime(endDate.atStartOfDay(ZoneOffset.UTC));
ArgChecker.isTrue(endTime >= 0d, "Option must be before expiry to compute an implied volatility");
double strike = period.getStrike();
double forward = ON_FUNCT.rate(onComputation, onComputation.getStartDate(), onComputation.getEndDate(), ratesProvider);
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);
return sabrVolatilities.getParameters().getSabrVolatilityFormula()
.volatility(forward + shift, strike + shift, endTime,
sabrAdjusted.getAlpha(), sabrAdjusted.getBeta(), sabrAdjusted.getRho(), sabrAdjusted.getNu());
}
//-------------------------------------------------------------------------
/**
* Computes the forward rate for the caplet/floorlet.
*
* @param period the caplet/floorlet period
* @param ratesProvider the rates provider
* @return the forward rate
*/
public double forwardRate(OvernightInArrearsCapletFloorletPeriod period, RatesProvider ratesProvider) {
OvernightCompoundedRateComputation onComputation = period.getOvernightRate();
return ON_FUNCT.rate(onComputation, onComputation.getStartDate(), onComputation.getEndDate(), ratesProvider);
}
}
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