Class LIBORCovarianceModelStochasticHestonVolatility

java.lang.Object

net.finmath.montecarlo.interestrate.models.covariance.AbstractLIBORCovarianceModel

net.finmath.montecarlo.interestrate.models.covariance.AbstractLIBORCovarianceModelParametric

net.finmath.montecarlo.interestrate.models.covariance.LIBORCovarianceModelStochasticHestonVolatility

All Implemented Interfaces:

Serializable, LIBORCovarianceModel, LIBORCovarianceModelCalibrateable, LIBORCovarianceModelParametric

public class LIBORCovarianceModelStochasticHestonVolatility
extends AbstractLIBORCovarianceModelParametric

As Heston like stochastic volatility model, using a process \( \lambda(t) = \sqrt(V(t)) \) \[ dV(t) = \kappa ( \theta - V(t) ) dt + \xi \sqrt{V(t)} dW_{1}(t), \quad V(0) = 1.0, \] where \( \lambda(0) = 1 \) to scale all factor loadings \( f_{i} \) returned by a given covariance model. The model constructed is \( \lambda(t) F(t) \) where \( \lambda(t) \) is a discretization of the above process and \( F = ( f_{1}, \ldots, f_{m} ) \) is the factor loading from the given covariance model. The process uses the first factor of the Brownian motion provided by an object implementing BrownianMotion. This can be used to generate correlations to other objects. If you like to reuse a factor of another Brownian motion use a BrownianMotionView to delegate \( ( \mathrm{d} W_{1}(t) ) \) to a different object. The parameter of this model is a joint parameter vector, consisting of the parameter vector of the given base covariance model and appending the parameters κ, θ and ξ at the end. If this model is not calibrateable, its parameter vector is that of the covariance model, i.e., ν and ρ will be not part of the calibration. For an illustration of its usage see the associated unit test.

Version:

1.0

Author:

Christian Fries

See Also:

• Serialized Form

Constructor Summary

Constructors

Constructor	Description
LIBORCovarianceModelStochasticHestonVolatility(AbstractLIBORCovarianceModelParametric covarianceModel, BrownianMotion brownianMotion, double kappa, double theta, double xi, boolean isCalibrateable)	Create a modification of a given AbstractLIBORCovarianceModelParametric with a stochastic volatility scaling.
LIBORCovarianceModelStochasticHestonVolatility(AbstractLIBORCovarianceModelParametric covarianceModel, BrownianMotion brownianMotion, RandomVariable kappa, RandomVariable theta, RandomVariable xi, boolean isCalibrateable)	Create a modification of a given AbstractLIBORCovarianceModelParametric with a stochastic volatility scaling.

Method Summary

Modifier and Type	Method	Description
Object	clone()
AbstractLIBORCovarianceModelParametric	getCloneWithModifiedData(Map<String,Object> dataModified)	Returns a clone of this model where the specified properties have been modified.
AbstractLIBORCovarianceModelParametric	getCloneWithModifiedParameters(double[] parameters)	Return an instance of this model using a new set of parameters.
AbstractLIBORCovarianceModelParametric	getCloneWithModifiedParameters(RandomVariable[] parameters)	Return an instance of this model using a new set of parameters.
RandomVariable[]	getFactorLoading(int timeIndex, int component, RandomVariable[] realizationAtTimeIndex)	Return the factor loading for a given time index and component index.
RandomVariable	getFactorLoadingPseudoInverse(int timeIndex, int component, int factor, RandomVariable[] realizationAtTimeIndex)	Returns the pseudo inverse of the factor matrix.
RandomVariable[]	getParameter()	Get the parameters of determining this parametric covariance model.
double[]	getParameterAsDouble()	Get the parameters of determining this parametric covariance model.

Methods inherited from class AbstractLIBORCovarianceModelParametric

getCloneCalibrated, getCloneCalibrated, getCloneCalibratedLegazy, toString

Methods inherited from class AbstractLIBORCovarianceModel

getCovariance, getCovariance, getFactorLoading, getFactorLoading, getLiborPeriodDiscretization, getNumberOfFactors, getTimeDiscretization

Methods inherited from class Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface LIBORCovarianceModel

getCovariance, getCovariance, getFactorLoading, getFactorLoading, getLiborPeriodDiscretization, getNumberOfFactors, getTimeDiscretization

Constructor Details

LIBORCovarianceModelStochasticHestonVolatility

public LIBORCovarianceModelStochasticHestonVolatility(AbstractLIBORCovarianceModelParametric covarianceModel,
 BrownianMotion brownianMotion,
 RandomVariable kappa,
 RandomVariable theta,
 RandomVariable xi,
 boolean isCalibrateable)

Create a modification of a given AbstractLIBORCovarianceModelParametric with a stochastic volatility scaling.

Parameters:

covarianceModel - A given AbstractLIBORCovarianceModelParametric.

brownianMotion - An object implementing BrownianMotion with at least two factors. This class uses the first two factors, but you may use BrownianMotionView to change this.

kappa - The initial value for κ, the mean reversion speed of the variance process V.

theta - The initial value for θ the mean reversion level of the variance process V.

xi - The initial value for ξ the volatility of the variance process V.

isCalibrateable - If true, the parameters ν and ρ are parameters. Note that the covariance model (covarianceModel) may have its own parameter calibration settings.

LIBORCovarianceModelStochasticHestonVolatility

public LIBORCovarianceModelStochasticHestonVolatility(AbstractLIBORCovarianceModelParametric covarianceModel,
 BrownianMotion brownianMotion,
 double kappa,
 double theta,
 double xi,
 boolean isCalibrateable)

Create a modification of a given AbstractLIBORCovarianceModelParametric with a stochastic volatility scaling.

Parameters:

covarianceModel - A given AbstractLIBORCovarianceModelParametric.

brownianMotion - An object implementing BrownianMotion with at least two factors. This class uses the first two factors, but you may use BrownianMotionView to change this.

kappa - The initial value for κ, the mean reversion speed of the variance process V.

theta - The initial value for θ the mean reversion level of the variance process V.

xi - The initial value for ξ the volatility of the variance process V.

isCalibrateable - If true, the parameters ν and ρ are parameters. Note that the covariance model (covarianceModel) may have its own parameter calibration settings.

Method Details

getParameter

public RandomVariable[] getParameter()

Description copied from class: AbstractLIBORCovarianceModelParametric

Get the parameters of determining this parametric covariance model. The parameters are usually free parameters which may be used in calibration.

Specified by:

getParameter in interface LIBORCovarianceModelParametric

Overrides:

getParameter in class AbstractLIBORCovarianceModelParametric

Returns:

Parameter vector.

clone

public Object clone()

Specified by:

clone in class AbstractLIBORCovarianceModelParametric

getCloneWithModifiedParameters

public AbstractLIBORCovarianceModelParametric getCloneWithModifiedParameters(RandomVariable[] parameters)

Description copied from class: AbstractLIBORCovarianceModelParametric

Return an instance of this model using a new set of parameters. Note: To improve performance it is admissible to return the same instance of the object given that the parameters have not changed. Models should be immutable.

Specified by:

getCloneWithModifiedParameters in interface LIBORCovarianceModelParametric

Overrides:

getCloneWithModifiedParameters in class AbstractLIBORCovarianceModelParametric

Parameters:

parameters - The new set of parameters.

Returns:

An instance of AbstractLIBORCovarianceModelParametric with modified parameters.

getCloneWithModifiedParameters

public AbstractLIBORCovarianceModelParametric getCloneWithModifiedParameters(double[] parameters)

Description copied from class: AbstractLIBORCovarianceModelParametric

Return an instance of this model using a new set of parameters. Note: To improve performance it is admissible to return the same instance of the object given that the parameters have not changed. Models should be immutable.

Specified by:

getCloneWithModifiedParameters in interface LIBORCovarianceModelParametric

Specified by:

getCloneWithModifiedParameters in class AbstractLIBORCovarianceModelParametric

Parameters:

parameters - The new set of parameters.

Returns:

An instance of AbstractLIBORCovarianceModelParametric with modified parameters.

getParameterAsDouble

public double[] getParameterAsDouble()

Description copied from class: AbstractLIBORCovarianceModelParametric

Get the parameters of determining this parametric covariance model. The parameters are usually free parameters which may be used in calibration.

Specified by:

getParameterAsDouble in interface LIBORCovarianceModelParametric

Specified by:

getParameterAsDouble in class AbstractLIBORCovarianceModelParametric

Returns:

Parameter vector.

getFactorLoading

public RandomVariable[] getFactorLoading(int timeIndex,
 int component,
 RandomVariable[] realizationAtTimeIndex)

Description copied from interface: LIBORCovarianceModel

Return the factor loading for a given time index and component index. The factor loading is the vector f_i such that the scalar product
f_jf_k = f_j,1f_k,1 + ... + f_j,mf_k,m
is the instantaneous covariance of the component j and k.

Specified by:

getFactorLoading in interface LIBORCovarianceModel

Specified by:

getFactorLoading in class AbstractLIBORCovarianceModel

Parameters:

timeIndex - The time index at which factor loading is requested.

component - The index of the component i.

realizationAtTimeIndex - The realization of the stochastic process (may be used to implement local volatility/covariance/correlation models).

Returns:

The factor loading f_i(t).

getFactorLoadingPseudoInverse

public RandomVariable getFactorLoadingPseudoInverse(int timeIndex,
 int component,
 int factor,
 RandomVariable[] realizationAtTimeIndex)

Description copied from interface: LIBORCovarianceModel

Returns the pseudo inverse of the factor matrix.

Specified by:

getFactorLoadingPseudoInverse in interface LIBORCovarianceModel

Specified by:

getFactorLoadingPseudoInverse in class AbstractLIBORCovarianceModel

Parameters:

timeIndex - The time index at which factor loading inverse is requested.

component - The index of the component i.

factor - The index of the factor j.

realizationAtTimeIndex - The realization of the stochastic process (may be used to implement local volatility/covariance/correlation models).

Returns:

The entry of the pseudo-inverse of the factor loading matrix.

getCloneWithModifiedData

public AbstractLIBORCovarianceModelParametric getCloneWithModifiedData(Map<String,Object> dataModified)
                                                                throws CalculationException

Description copied from interface: LIBORCovarianceModel

Returns a clone of this model where the specified properties have been modified. Note that there is no guarantee that a model reacts on a specification of a properties in the parameter map dataModified. If data is provided which is ignored by the model no exception may be thrown. Furthermore the structure of the covariance model has to match changed data. A change of the time discretizations may requires a change in the parameters but this function will just insert the new time discretization without changing the parameters. An exception may not be thrown.

Specified by:

getCloneWithModifiedData in interface LIBORCovarianceModel

Specified by:

getCloneWithModifiedData in class AbstractLIBORCovarianceModel

Parameters:

dataModified - Key-value-map of parameters to modify.

Returns:

A clone of this model (or a new instance of this model if no parameter was modified).

Throws:

CalculationException - Thrown when the model could not be created.