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

Class SsviVolatilityFunction

java.lang.Object

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

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

All Implemented Interfaces:

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

public final class SsviVolatilityFunction
extends VolatilityFunctionProvider<SsviFormulaData>
implements org.joda.beans.ImmutableBean, Serializable

Surface Stochastic Volatility Inspired (SSVI) formula.

Reference: Gatheral, Jim and Jacquier, Antoine. Arbitrage-free SVI volatility surfaces. arXiv:1204.0646v4, 2013. Section 4.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static SsviVolatilityFunction	DEFAULT	Default implementation.
static double	MIN_TIME_TO_EXPIRY	SSVI volatility description diverge for theta -> 0.

Method Summary

Modifier and Type	Method	Description
boolean	equals(Object obj)
int	hashCode()
static org.joda.beans.TypedMetaBean<SsviVolatilityFunction>	meta()	The meta-bean for SsviVolatilityFunction.
org.joda.beans.TypedMetaBean<SsviVolatilityFunction>	metaBean()
String	toString()
double	volatility(double forward, double strike, double timeToExpiry, SsviFormulaData data)	Calculates the volatility.
ValueDerivatives	volatilityAdjoint(double forward, double strike, double timeToExpiry, SsviFormulaData data)	Computes the implied volatility in the SSVI formula and its derivatives.
double	volatilityAdjoint2(double forward, double strike, double timeToExpiry, SsviFormulaData data, double[] volatilityD, double[][] volatilityD2)	Computes the first and second order derivatives of the volatility.

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 SsviVolatilityFunction DEFAULT

Default implementation.

MIN_TIME_TO_EXPIRY

public static final double MIN_TIME_TO_EXPIRY

SSVI volatility description diverge for theta -> 0. Lower bound for which time to expiry is accepted.

See Also:

Constant Field Values

Method Detail

volatility

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

Description copied from class: VolatilityFunctionProvider

Calculates the volatility.

Specified by:

volatility in class VolatilityFunctionProvider<SsviFormulaData>

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

volatilityAdjoint

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

Computes the implied volatility in the SSVI formula 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 time to expiry
• [3] derivative with respect to the sigma (ATM volatility)
• [4] derivative with respect to the rho
• [5] derivative with respect to the eta

Overrides:

volatilityAdjoint in class VolatilityFunctionProvider<SsviFormulaData>

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 SSVI data

Returns:

the volatility and associated derivatives

volatilityAdjoint2

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

Description copied from class: VolatilityFunctionProvider

Computes the first and second order derivatives of the volatility.

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, then followed by model parameters. Thus the length of the array should be 2 + (number of model parameters).

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

Specified by:

volatilityAdjoint2 in class VolatilityFunctionProvider<SsviFormulaData>

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

volatilityD - the array used to return the first order derivative

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

Returns:

the volatility

meta

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

The meta-bean for SsviVolatilityFunction.

Returns:

the meta-bean, not null

metaBean

public org.joda.beans.TypedMetaBean<SsviVolatilityFunction> 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