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

Class SabrHaganVolatilityFunctionProvider

java.lang.Object

com.opengamma.strata.pricer.impl.volatility.smile.VolatilityFunctionProvider<SabrFormulaData>

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

All Implemented Interfaces:

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

public final class SabrHaganVolatilityFunctionProvider
extends VolatilityFunctionProvider<SabrFormulaData>
implements SabrVolatilityFormula, org.joda.beans.ImmutableBean, Serializable

The Hagan SABR volatility function provider.

This class provides the functions of volatility and its sensitivity to the SABR model parameters based on the original Hagan SABR formula.

Reference: Hagan, P.; Kumar, D.; Lesniewski, A. & Woodward, D. "Managing smile risk", Wilmott Magazine, 2002, September, 84-108

OpenGamma documentation: SABR Implementation, OpenGamma documentation n. 33, April 2016.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static SabrHaganVolatilityFunctionProvider	DEFAULT Default implementation.

Method Summary

Modifier and Type	Method and Description
boolean	equals(Object obj)
ValueType	getVolatilityType() Gets the type of volatility returned by the SabrVolatilityFormula.volatility(double, double, double, double, double, double, double) method.
int	hashCode()
static org.joda.beans.TypedMetaBean<SabrHaganVolatilityFunctionProvider>	meta() The meta-bean for SabrHaganVolatilityFunctionProvider.
org.joda.beans.TypedMetaBean<SabrHaganVolatilityFunctionProvider>	metaBean()
String	toString()
double	volatility(double forward, double strike, double timeToExpiry, double alpha, double beta, double rho, double nu) Calculates the volatility.
double	volatility(double forward, double strike, double timeToExpiry, SabrFormulaData data) Calculates the volatility.
ValueDerivatives	volatilityAdjoint(double forward, double strike, double timeToExpiry, double alpha, double beta, double rho, double nu) Computes the implied volatility in the SABR model and its derivatives.
ValueDerivatives	volatilityAdjoint(double forward, double strike, double timeToExpiry, SabrFormulaData data) Computes the implied volatility in the SABR model and its derivatives.
double	volatilityAdjoint2(double forward, double strike, double timeToExpiry, SabrFormulaData data, double[] volatilityD, double[][] volatilityD2) Computes the first and second order derivatives of the Black implied volatility in the SABR model.

Methods inherited from class java.lang.Object

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

Methods inherited from interface com.opengamma.strata.pricer.model.SabrVolatilityFormula

hagan

Methods inherited from interface org.joda.beans.Bean

property, propertyNames

Field Detail

DEFAULT

public static final SabrHaganVolatilityFunctionProvider DEFAULT

Default implementation.

Method Detail

getVolatilityType

public ValueType getVolatilityType()

Description copied from interface: SabrVolatilityFormula

Gets the type of volatility returned by the SabrVolatilityFormula.volatility(double, double, double, double, double, double, double) method.

Specified by:

getVolatilityType in interface SabrVolatilityFormula

Returns:

the type

volatility

public double volatility(double forward,
                         double strike,
                         double timeToExpiry,
                         SabrFormulaData data)

Description copied from class: VolatilityFunctionProvider

Calculates the volatility.

Specified by:

volatility in class VolatilityFunctionProvider<SabrFormulaData>

Parameters:

forward - the forward value of the underlying

strike - the strike value of the option

timeToExpiry - the time to expiry of the option

data - the model data

Returns:

the volatility

volatility

public double volatility(double forward,
                         double strike,
                         double timeToExpiry,
                         double alpha,
                         double beta,
                         double rho,
                         double nu)

Description copied from interface: SabrVolatilityFormula

Calculates the volatility.

Specified by:

volatility in interface SabrVolatilityFormula

Parameters:

forward - the forward value of the underlying

strike - the strike value of the option

timeToExpiry - the time to expiry of the option

alpha - the SABR alpha value

beta - the SABR beta value

rho - the SABR rho value

nu - the SABR nu value

Returns:

the volatility

volatilityAdjoint

public ValueDerivatives volatilityAdjoint(double forward,
                                          double strike,
                                          double timeToExpiry,
                                          SabrFormulaData data)

Computes the implied volatility in the SABR model and its derivatives.

The derivatives are stored in an array with:

• [0] derivative with respect to the forward
• [1] derivative with respect to the strike
• [2] derivative with respect to the alpha
• [3] derivative with respect to the beta
• [4] derivative with respect to the rho
• [5] derivative with respect to the nu

Overrides:

volatilityAdjoint in class VolatilityFunctionProvider<SabrFormulaData>

Parameters:

forward - the forward value of the underlying

strike - the strike value of the option

timeToExpiry - the time to expiry of the option

data - the SABR data

Returns:

the volatility and associated derivatives

volatilityAdjoint

public ValueDerivatives volatilityAdjoint(double forward,
                                          double strike,
                                          double timeToExpiry,
                                          double alpha,
                                          double beta,
                                          double rho,
                                          double nu)

Computes the implied volatility in the SABR model and its derivatives.

The derivatives are stored in an array with:

• [0] derivative with respect to the forward
• [1] derivative with respect to the strike
• [2] derivative with respect to the alpha
• [3] derivative with respect to the beta
• [4] derivative with respect to the rho
• [5] derivative with respect to the nu

Specified by:

volatilityAdjoint in interface SabrVolatilityFormula

Parameters:

forward - the forward value of the underlying

strike - the strike value of the option

timeToExpiry - the time to expiry of the option

alpha - the SABR alpha value

beta - the SABR beta value

rho - the SABR rho value

nu - the SABR nu value

Returns:

the volatility and associated derivatives

volatilityAdjoint2

public double volatilityAdjoint2(double forward,
                                 double strike,
                                 double timeToExpiry,
                                 SabrFormulaData data,
                                 double[] volatilityD,
                                 double[][] volatilityD2)

Computes the first and second order derivatives of the Black implied volatility in the SABR model.

The first derivative values will be stored in the input array volatilityD The array contains, [0] Derivative w.r.t the forward, [1] the derivative w.r.t the strike, [2] the derivative w.r.t. to alpha, [3] the derivative w.r.t. to beta, [4] the derivative w.r.t. to rho, and [5] the derivative w.r.t. to nu. Thus the length of the array should be 6.

The second derivative values will be stored in the input array volatilityD2. Only the second order derivative with respect to the forward and strike are implemented. The array contains [0][0] forward-forward; [0][1] forward-strike; [1][1] strike-strike. Thus the size should be 2 x 2.

Around ATM, a first order expansion is used to due to some 0/0-type indetermination. The second order derivative produced is poor around ATM.

Specified by:

volatilityAdjoint2 in class VolatilityFunctionProvider<SabrFormulaData>

Parameters:

forward - the forward value of the underlying

strike - the strike value of the option

timeToExpiry - the time to expiry of the option

data - the SABR data.

volatilityD - the array used to return the first order derivative

volatilityD2 - the array of array used to return the second order derivative

Returns:

the Black implied volatility

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object

toString

public String toString()

Overrides:

toString in class Object

meta

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

The meta-bean for SabrHaganVolatilityFunctionProvider.

Returns:

the meta-bean, not null

metaBean

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

Specified by:

metaBean in interface org.joda.beans.Bean