com.opengamma.strata.pricer.impl.rate.model

Class HullWhiteOneFactorPiecewiseConstantInterestRateModel

java.lang.Object

com.opengamma.strata.pricer.impl.rate.model.HullWhiteOneFactorPiecewiseConstantInterestRateModel

All Implemented Interfaces:

Serializable, org.joda.beans.Bean, org.joda.beans.ImmutableBean

public final class HullWhiteOneFactorPiecewiseConstantInterestRateModel
extends Object
implements org.joda.beans.ImmutableBean, Serializable

Methods related to the Hull-White one factor (extended Vasicek) model with piecewise constant volatility.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static HullWhiteOneFactorPiecewiseConstantInterestRateModel	DEFAULT Default instance.

Method Summary

Modifier and Type	Method and Description
double	alpha(HullWhiteOneFactorPiecewiseConstantParameters data, double startExpiry, double endExpiry, double numeraireTime, double bondMaturity) Calculates the (zero-coupon) bond volatility divided by a bond numeraire, i.e., alpha, for a given period.
ValueDerivatives	alphaAdjoint(HullWhiteOneFactorPiecewiseConstantParameters data, double startExpiry, double endExpiry, double numeraireTime, double bondMaturity) Calculates the (zero-coupon) bond volatility divided by a bond numeraire, i.e., alpha, for a given period and its derivatives.
double	beta(HullWhiteOneFactorPiecewiseConstantParameters data, double startExpiry, double endExpiry) Calculates the beta parameter.
boolean	equals(Object obj)
double	futuresConvexityFactor(HullWhiteOneFactorPiecewiseConstantParameters data, double t0, double t1, double t2) Calculates the future convexity factor used in future pricing.
ValueDerivatives	futuresConvexityFactorAdjoint(HullWhiteOneFactorPiecewiseConstantParameters data, double t0, double t1, double t2) Calculates the future convexity factor and its derivatives with respect to the model volatilities.
int	hashCode()
double	kappa(DoubleArray discountedCashFlow, DoubleArray alpha) Calculates the exercise boundary for swaptions.
double	lambda(DoubleArray discountedCashFlow, DoubleArray alpha2, DoubleArray hwH) Calculates the common part of the exercise boundary of European swaptions forward.
static org.joda.beans.TypedMetaBean<HullWhiteOneFactorPiecewiseConstantInterestRateModel>	meta() The meta-bean for HullWhiteOneFactorPiecewiseConstantInterestRateModel.
org.joda.beans.TypedMetaBean<HullWhiteOneFactorPiecewiseConstantInterestRateModel>	metaBean()
double	paymentDelayConvexityFactor(HullWhiteOneFactorPiecewiseConstantParameters parameters, double startExpiry, double endExpiry, double u, double v, double tp) Calculates the payment delay convexity factor used in coupons with mismatched dates pricing.
double	swapRate(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the swap rate for a given value of the standard normal random variable in the P(*,theta) numeraire.
ValueDerivatives	swapRateDaf1(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the first order derivative of the swap rate with respect to the alphaFixed in the P(*,theta) numeraire.
ValueDerivatives	swapRateDai1(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the first order derivative of the swap rate with respect to the alphaIbor in the P(*,theta) numeraire.
ValueDerivatives	swapRateDdcff1(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the first order derivative of the swap rate with respect to the discountedCashFlowFixed in the P(*,theta) numeraire.
ValueDerivatives	swapRateDdcfi1(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the first order derivative of the swap rate with respect to the discountedCashFlowIbor in the P(*,theta) numeraire.
double	swapRateDx1(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the first order derivative of the swap rate with respect to the value of the standard normal random variable in the P(*,theta) numeraire.
double	swapRateDx2(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the second order derivative of the swap rate with respect to the value of the standard normal random variable in the P(*,theta) numeraire.
Pair<DoubleArray,DoubleArray>	swapRateDx2Da1(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the first order derivative with respect to the alphaFixed and to the alphaIbor of the of swap rate second derivative with respect to the random variable x in the P(*,theta) numeraire.
Pair<DoubleArray,DoubleArray>	swapRateDx2Ddcf1(double x, DoubleArray discountedCashFlowFixed, DoubleArray alphaFixed, DoubleArray discountedCashFlowIbor, DoubleArray alphaIbor) Calculates the first order derivative with respect to the discountedCashFlowFixed and to the discountedCashFlowIbor of the of swap rate second derivative with respect to the random variable x in the P(*,theta) numeraire.
String	toString()
DoubleMatrix	volatilityMaturityPart(HullWhiteOneFactorPiecewiseConstantParameters hwParameters, double u, DoubleMatrix v) Calculates the maturity dependent part of the volatility (function called H in the implementation note).

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.joda.beans.Bean

property, propertyNames

Field Detail

DEFAULT

public static final HullWhiteOneFactorPiecewiseConstantInterestRateModel DEFAULT

Default instance.

Method Detail

futuresConvexityFactor

public double futuresConvexityFactor(HullWhiteOneFactorPiecewiseConstantParameters data,
                                     double t0,
                                     double t1,
                                     double t2)

Calculates the future convexity factor used in future pricing.

The factor is called gamma in the reference: Henrard, M. "The Irony in the derivatives discounting Part II: the crisis", Wilmott Journal, 2010, 2, 301-316

Parameters:

data - the Hull-White model parameters

t0 - the first expiry time

t1 - the first reference time

t2 - the second reference time

Returns:

the factor

futuresConvexityFactorAdjoint

public ValueDerivatives futuresConvexityFactorAdjoint(HullWhiteOneFactorPiecewiseConstantParameters data,
                                                      double t0,
                                                      double t1,
                                                      double t2)

Calculates the future convexity factor and its derivatives with respect to the model volatilities.

The factor is called gamma in the reference: Henrard, M. "The Irony in the derivatives discounting Part II: the crisis", Wilmott Journal, 2010, 2, 301-316

Parameters:

data - the Hull-White model parameters

t0 - the expiry time

t1 - the first reference time

t2 - the second reference time

Returns:

the factor and drivatives

paymentDelayConvexityFactor

public double paymentDelayConvexityFactor(HullWhiteOneFactorPiecewiseConstantParameters parameters,
                                          double startExpiry,
                                          double endExpiry,
                                          double u,
                                          double v,
                                          double tp)

Calculates the payment delay convexity factor used in coupons with mismatched dates pricing.

Parameters:

parameters - the Hull-White model parameters

startExpiry - the start expiry time

endExpiry - the end expiry time

u - the fixing period start time

v - the fixing period end time

tp - the payment time

Returns:

the factor

alpha

public double alpha(HullWhiteOneFactorPiecewiseConstantParameters data,
                    double startExpiry,
                    double endExpiry,
                    double numeraireTime,
                    double bondMaturity)

Calculates the (zero-coupon) bond volatility divided by a bond numeraire, i.e., alpha, for a given period.

Parameters:

data - the Hull-White model data

startExpiry - the start time of the expiry period

endExpiry - the end time of the expiry period

numeraireTime - the time to maturity for the bond numeraire

bondMaturity - the time to maturity for the bond

Returns:

the re-based bond volatility

alphaAdjoint

public ValueDerivatives alphaAdjoint(HullWhiteOneFactorPiecewiseConstantParameters data,
                                     double startExpiry,
                                     double endExpiry,
                                     double numeraireTime,
                                     double bondMaturity)

Calculates the (zero-coupon) bond volatility divided by a bond numeraire, i.e., alpha, for a given period and its derivatives.

The derivative values are the derivatives of the function alpha with respect to the piecewise constant volatilities.

Parameters:

data - the Hull-White model data

startExpiry - the start time of the expiry period

endExpiry - the end time of the expiry period

numeraireTime - the time to maturity for the bond numeraire

bondMaturity - the time to maturity for the bond

Returns:

The re-based bond volatility

kappa

public double kappa(DoubleArray discountedCashFlow,
                    DoubleArray alpha)

Calculates the exercise boundary for swaptions.

Reference: Henrard, M. (2003). "Explicit bond option and swaption formula in Heath-Jarrow-Morton one-factor model". International Journal of Theoretical and Applied Finance, 6(1):57--72.

Parameters:

discountedCashFlow - the cash flow equivalent discounted to today

alpha - the zero-coupon bond volatilities

Returns:

the exercise boundary

beta

public double beta(HullWhiteOneFactorPiecewiseConstantParameters data,
                   double startExpiry,
                   double endExpiry)

Calculates the beta parameter.

This is intended to be used in particular for Bermudan swaption first step of the pricing.

Reference: Henrard, "M. Bermudan Swaptions in Gaussian HJM One-Factor Model: Analytical and Numerical Approaches". SSRN, October 2008. Available at SSRN: http://ssrn.com/abstract=1287982

Parameters:

data - the Hull-White model data

startExpiry - the start time of the expiry period

endExpiry - the end time of the expiry period

Returns:

the re-based bond volatility

lambda

public double lambda(DoubleArray discountedCashFlow,
                     DoubleArray alpha2,
                     DoubleArray hwH)

Calculates the common part of the exercise boundary of European swaptions forward.

This is intended to be used in particular for Bermudan swaption first step of the pricing.

Reference: Henrard, "M. Bermudan Swaptions in Gaussian HJM One-Factor Model: Analytical and Numerical Approaches". SSRN, October 2008. Available at SSRN: http://ssrn.com/abstract=1287982

Parameters:

discountedCashFlow - the swap discounted cash flows

alpha2 - square of the alpha parameter

hwH - the H factors

Returns:

the exercise boundary

volatilityMaturityPart

public DoubleMatrix volatilityMaturityPart(HullWhiteOneFactorPiecewiseConstantParameters hwParameters,
                                           double u,
                                           DoubleMatrix v)

Calculates the maturity dependent part of the volatility (function called H in the implementation note).

Parameters:

hwParameters - the model parameters

u - the start time

v - the end time

Returns:

the volatility

swapRate

public double swapRate(double x,
                       DoubleArray discountedCashFlowFixed,
                       DoubleArray alphaFixed,
                       DoubleArray discountedCashFlowIbor,
                       DoubleArray alphaIbor)

Calculates the swap rate for a given value of the standard normal random variable in the P(*,theta) numeraire.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the swap rate

swapRateDx1

public double swapRateDx1(double x,
                          DoubleArray discountedCashFlowFixed,
                          DoubleArray alphaFixed,
                          DoubleArray discountedCashFlowIbor,
                          DoubleArray alphaIbor)

Calculates the first order derivative of the swap rate with respect to the value of the standard normal random variable in the P(*,theta) numeraire.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the first derivative of the swap rate

swapRateDx2

public double swapRateDx2(double x,
                          DoubleArray discountedCashFlowFixed,
                          DoubleArray alphaFixed,
                          DoubleArray discountedCashFlowIbor,
                          DoubleArray alphaIbor)

Calculates the second order derivative of the swap rate with respect to the value of the standard normal random variable in the P(*,theta) numeraire.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the second derivative of the swap rate

swapRateDdcfi1

public ValueDerivatives swapRateDdcfi1(double x,
                                       DoubleArray discountedCashFlowFixed,
                                       DoubleArray alphaFixed,
                                       DoubleArray discountedCashFlowIbor,
                                       DoubleArray alphaIbor)

Calculates the first order derivative of the swap rate with respect to the discountedCashFlowIbor in the P(*,theta) numeraire.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the swap rate and derivatives

swapRateDdcff1

public ValueDerivatives swapRateDdcff1(double x,
                                       DoubleArray discountedCashFlowFixed,
                                       DoubleArray alphaFixed,
                                       DoubleArray discountedCashFlowIbor,
                                       DoubleArray alphaIbor)

Calculates the first order derivative of the swap rate with respect to the discountedCashFlowFixed in the P(*,theta) numeraire.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the swap rate and derivatives

swapRateDai1

public ValueDerivatives swapRateDai1(double x,
                                     DoubleArray discountedCashFlowFixed,
                                     DoubleArray alphaFixed,
                                     DoubleArray discountedCashFlowIbor,
                                     DoubleArray alphaIbor)

Calculates the first order derivative of the swap rate with respect to the alphaIbor in the P(*,theta) numeraire.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the swap rate and derivatives

swapRateDaf1

public ValueDerivatives swapRateDaf1(double x,
                                     DoubleArray discountedCashFlowFixed,
                                     DoubleArray alphaFixed,
                                     DoubleArray discountedCashFlowIbor,
                                     DoubleArray alphaIbor)

Calculates the first order derivative of the swap rate with respect to the alphaFixed in the P(*,theta) numeraire.

Parameters:

x - the random variable value.

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the swap rate and derivatives

swapRateDx2Ddcf1

public Pair<DoubleArray,DoubleArray> swapRateDx2Ddcf1(double x,
                                                      DoubleArray discountedCashFlowFixed,
                                                      DoubleArray alphaFixed,
                                                      DoubleArray discountedCashFlowIbor,
                                                      DoubleArray alphaIbor)

Calculates the first order derivative with respect to the discountedCashFlowFixed and to the discountedCashFlowIbor of the of swap rate second derivative with respect to the random variable x in the P(*,theta) numeraire.

The result is made of a pair of arrays. The first one is the derivative with respect to discountedCashFlowFixed and the second one with respect to discountedCashFlowIbor.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the swap rate derivatives

swapRateDx2Da1

public Pair<DoubleArray,DoubleArray> swapRateDx2Da1(double x,
                                                    DoubleArray discountedCashFlowFixed,
                                                    DoubleArray alphaFixed,
                                                    DoubleArray discountedCashFlowIbor,
                                                    DoubleArray alphaIbor)

Calculates the first order derivative with respect to the alphaFixed and to the alphaIbor of the of swap rate second derivative with respect to the random variable x in the P(*,theta) numeraire.

The result is made of a pair of arrays. The first one is the derivative with respect to alphaFixed and the second one with respect to alphaIbor.

Parameters:

x - the random variable value

discountedCashFlowFixed - the discounted cash flows equivalent of the swap fixed leg

alphaFixed - the zero-coupon bond volatilities for the swap fixed leg

discountedCashFlowIbor - the discounted cash flows equivalent of the swap Ibor leg

alphaIbor - the zero-coupon bond volatilities for the swap Ibor leg

Returns:

the swap rate derivatives

meta

public static org.joda.beans.TypedMetaBean<HullWhiteOneFactorPiecewiseConstantInterestRateModel> meta()

The meta-bean for HullWhiteOneFactorPiecewiseConstantInterestRateModel.

Returns:

the meta-bean, not null

metaBean

public org.joda.beans.TypedMetaBean<HullWhiteOneFactorPiecewiseConstantInterestRateModel> metaBean()

Specified by:

metaBean in interface org.joda.beans.Bean

equals

public boolean equals(Object obj)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

toString

public String toString()

Overrides:

toString in class Object