Package com.opengamma.strata.pricer.impl.volatility.smile

Class SabrInArrearsVolatilityFunction

java.lang.Object

com.opengamma.strata.pricer.impl.volatility.smile.SabrInArrearsVolatilityFunction

All Implemented Interfaces:

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

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

Adjustments to the SABR parameters to accommodate the pricing of in-arrears caplets.

The parameter "q" in the formula is a parameter such that 1-q is closely related to a mean reversion. It is defaulted to q=1 in the default instance of the formula.

Reference: Willems, Sander. SABR smiles for RFR caplets. August 2020. Electronic copy available at: https://ssrn.com/abstract=3567655

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	SabrInArrearsVolatilityFunction.Builder	The bean-builder for SabrInArrearsVolatilityFunction.
static class	SabrInArrearsVolatilityFunction.Meta	The meta-bean for SabrInArrearsVolatilityFunction.

Field Summary

Fields

Modifier and Type	Field	Description
static SabrInArrearsVolatilityFunction	DEFAULT	Default implementation with q = 1;

Method Summary

Modifier and Type	Method	Description
static SabrInArrearsVolatilityFunction.Builder	builder()	Returns a builder used to create an instance of the bean.
SabrFormulaData	effectiveSabr(SabrFormulaData parameters, double tau0, double tau1)	The effective SABR parameters from the raw SABR parameters and the times.
List<ValueDerivatives>	effectiveSabrAd(SabrFormulaData parameters, double tau0, double tau1)	The effective SABR parameters from the raw SABR parameters and the times.
SabrFormulaData	effectiveSabrAfterStart(SabrFormulaData parameters, double tau0, double tau1)	The effective SABR parameters from the raw SABR parameters and the times.
List<ValueDerivatives>	effectiveSabrAfterStartAd(SabrFormulaData parameters, double tau0, double tau1)	The effective SABR parameters and their derivatives from the raw SABR parameters and the times.
SabrFormulaData	effectiveSabrBeforeStart(SabrFormulaData parameters, double tau0, double tau1)	The effective SABR parameters from the raw SABR parameters and the times.
List<ValueDerivatives>	effectiveSabrBeforeStartAd(SabrFormulaData parameters, double tau0, double tau1)	The effective SABR parameters and their derivatives from the raw SABR parameters and the times.
boolean	equals(Object obj)
double	getQ()	Gets the mean reversion related parameter.
int	hashCode()
static SabrInArrearsVolatilityFunction.Meta	meta()	The meta-bean for SabrInArrearsVolatilityFunction.
SabrInArrearsVolatilityFunction.Meta	metaBean()
static SabrInArrearsVolatilityFunction	of(double q)	Obtains an instance.
SabrInArrearsVolatilityFunction.Builder	toBuilder()	Returns a builder that allows this bean to be mutated.
String	toString()

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 SabrInArrearsVolatilityFunction DEFAULT

Default implementation with q = 1;

Method Detail

effectiveSabrBeforeStart

public SabrFormulaData effectiveSabrBeforeStart(SabrFormulaData parameters,
                                                double tau0,
                                                double tau1)

The effective SABR parameters from the raw SABR parameters and the times. Formula in the case tau0 > 0.

Theorem 4.2 in reference.

Parameters:

parameters - the raw SABR parameters

tau0 - the accumulation period start time

tau1 - the accumulation period end time

Returns:

the effective SABR parameters

effectiveSabrAfterStart

public SabrFormulaData effectiveSabrAfterStart(SabrFormulaData parameters,
                                               double tau0,
                                               double tau1)

The effective SABR parameters from the raw SABR parameters and the times. Formula in the case tau0 <= 0.

Theorem 4.1 in reference.

Parameters:

parameters - the raw SABR parameters

tau0 - the accumulation period start time

tau1 - the accumulation period end time

Returns:

the effective SABR parameters

effectiveSabr

public SabrFormulaData effectiveSabr(SabrFormulaData parameters,
                                     double tau0,
                                     double tau1)

The effective SABR parameters from the raw SABR parameters and the times.

Parameters:

parameters - the raw SABR parameters

tau0 - the accumulation period start time

tau1 - the accumulation period end time

Returns:

the effective SABR parameters

effectiveSabrAfterStartAd

public List<ValueDerivatives> effectiveSabrAfterStartAd(SabrFormulaData parameters,
                                                        double tau0,
                                                        double tau1)

The effective SABR parameters and their derivatives from the raw SABR parameters and the times. Formula in the case tau0 <= 0;

The results are provided as a list of ValueDerivatives corresponding to alpha, beta, rho and nu and with each derivatives part containing the derivatives with respect to alpha, beta, rho, nu, tau0 and tau1.

Parameters:

parameters - the raw SABR parameters

tau0 - the accumulation period start time

tau1 - the accumulation period end time

Returns:

the effective SABR parameters

effectiveSabrBeforeStartAd

public List<ValueDerivatives> effectiveSabrBeforeStartAd(SabrFormulaData parameters,
                                                         double tau0,
                                                         double tau1)

The effective SABR parameters and their derivatives from the raw SABR parameters and the times. Formula in the case tau0 > 0;

The results are provided as a list of ValueDerivatives corresponding to alpha, beta, rho and nu and with each derivatives part containing the derivatives with respect to alpha, beta, rho, nu, tau0 and tau1.

Parameters:

parameters - the raw SABR parameters

tau0 - the accumulation period start time

tau1 - the accumulation period end time

Returns:

the effective SABR parameters

effectiveSabrAd

public List<ValueDerivatives> effectiveSabrAd(SabrFormulaData parameters,
                                              double tau0,
                                              double tau1)

The effective SABR parameters from the raw SABR parameters and the times.

Parameters:

parameters - the raw SABR parameters

tau0 - the accumulation period start time

tau1 - the accumulation period end time

Returns:

the effective SABR parameters

meta

public static SabrInArrearsVolatilityFunction.Meta meta()

The meta-bean for SabrInArrearsVolatilityFunction.

Returns:

the meta-bean, not null

of

public static SabrInArrearsVolatilityFunction of(double q)

Obtains an instance.

Parameters:

q - the value of the property

Returns:

the instance

builder

public static SabrInArrearsVolatilityFunction.Builder builder()

Returns a builder used to create an instance of the bean.

Returns:

the builder, not null

metaBean

public SabrInArrearsVolatilityFunction.Meta metaBean()

Specified by:

metaBean in interface org.joda.beans.Bean

getQ

public double getQ()

Gets the mean reversion related parameter.

Returns:

the value of the property

toBuilder

public SabrInArrearsVolatilityFunction.Builder toBuilder()

Returns a builder that allows this bean to be mutated.

Returns:

the mutable builder, not null

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