Class FDMBatesModel

java.lang.Object

net.finmath.finitedifference.assetderivativevaluation.models.FDMHestonModel

net.finmath.finitedifference.assetderivativevaluation.models.FDMBatesModel

All Implemented Interfaces:

FiniteDifferenceBoundary, FiniteDifferenceEquityModel, FiniteDifferenceModel, Model

public class FDMBatesModel
extends FDMHestonModel

Finite difference model for option pricing under the Bates stochastic volatility jump-diffusion model.

State variables are (S, v) where S is the spot and v is the instantaneous variance.

The local part of the model coincides with the Heston model, while the jump part is supplied separately through getJumpComponent().

Hence:

• FDMHestonModel.getDrift(double, double...) returns the local drift vector of the state variables, inherited from FDMHestonModel,
• FDMHestonModel.getFactorLoading(double, double...) returns the local factor loading matrix, inherited from FDMHestonModel,
• getJumpComponent() returns the finite-activity Bates jump component acting on the spot variable.

The constructor argument order follows the Heston constructors first and then appends the jump parameters.

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
FDMBatesModel(double initialSpot, double initialVariance, double riskFreeRate, double dividendYieldRate, double kappa, double thetaV, double sigma, double rho, double jumpIntensity, double jumpMean, double jumpStdDev, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model from constant rates and jump parameters.
FDMBatesModel(double initialSpot, double initialVariance, double riskFreeRate, double kappa, double thetaV, double sigma, double rho, double jumpIntensity, double jumpMean, double jumpStdDev, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model from a constant risk-free rate and zero dividend yield, using jump parameters.
FDMBatesModel(double initialSpot, double initialVariance, double riskFreeRate, double dividendYieldRate, double kappa, double thetaV, double sigma, double rho, BatesJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model from constant rates and an explicit jump component.
FDMBatesModel(double initialSpot, double initialVariance, double riskFreeRate, double kappa, double thetaV, double sigma, double rho, BatesJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model from a constant risk-free rate and zero dividend yield, using an explicit jump component.
FDMBatesModel(double initialSpot, double initialVariance, DiscountCurve riskFreeCurve, double kappa, double thetaV, double sigma, double rho, double jumpIntensity, double jumpMean, double jumpStdDev, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model without dividend yield curve, using jump parameters.
FDMBatesModel(double initialSpot, double initialVariance, DiscountCurve riskFreeCurve, double kappa, double thetaV, double sigma, double rho, BatesJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model without dividend yield curve, using an explicit jump component.
FDMBatesModel(double initialSpot, double initialVariance, DiscountCurve riskFreeCurve, DiscountCurve dividendYieldCurve, double kappa, double thetaV, double sigma, double rho, double jumpIntensity, double jumpMean, double jumpStdDev, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model from discount curves and jump parameters.
FDMBatesModel(double initialSpot, double initialVariance, DiscountCurve riskFreeCurve, DiscountCurve dividendYieldCurve, double kappa, double thetaV, double sigma, double rho, BatesJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)	Constructs a Bates finite difference model from discount curves and an explicit jump component.

Method Summary

Modifier and Type	Method	Description
BatesJumpComponent	getBatesJumpComponent()	Returns the Bates jump component.
FiniteDifferenceEquityModel	getCloneWithModifiedSpaceTimeDiscretization(SpaceTimeDiscretization newSpaceTimeDiscretization)	Returns a clone of this model with a modified space-time discretization.
Optional<JumpComponent>	getJumpComponent()	Returns the optional jump component of the infinitesimal generator.

Methods inherited from class FDMHestonModel

getBoundaryConditionsAtLowerBoundary, getBoundaryConditionsAtUpperBoundary, getCovariance, getDividendYieldCurve, getDrift, getFactorLoading, getInitialValue, getKappa, getRho, getRiskFreeCurve, getSigma, getSpaceTimeDiscretization, getThetaV

Methods inherited from class Object

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

Methods inherited from interface FiniteDifferenceEquityModel

getDividendYieldCurves

Constructor Details

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 DiscountCurve riskFreeCurve,
 DiscountCurve dividendYieldCurve,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 BatesJumpComponent jumpComponent,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model from discount curves and an explicit jump component.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeCurve - Risk-free discount curve.

dividendYieldCurve - Dividend yield discount curve.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpComponent - Bates jump component.

spaceTimeDiscretization - Grid object defining the spatial discretization.

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 DiscountCurve riskFreeCurve,
 DiscountCurve dividendYieldCurve,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 double jumpIntensity,
 double jumpMean,
 double jumpStdDev,
 double lowerIntegrationBound,
 double upperIntegrationBound,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model from discount curves and jump parameters.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeCurve - Risk-free discount curve.

dividendYieldCurve - Dividend yield discount curve.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpIntensity - Jump intensity.

jumpMean - Mean of the log-jump size.

jumpStdDev - Standard deviation of the log-jump size.

lowerIntegrationBound - Lower integration bound for the log-jump variable.

upperIntegrationBound - Upper integration bound for the log-jump variable.

spaceTimeDiscretization - Grid object defining the spatial discretization.

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 DiscountCurve riskFreeCurve,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 BatesJumpComponent jumpComponent,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model without dividend yield curve, using an explicit jump component.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeCurve - Risk-free discount curve.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpComponent - Bates jump component.

spaceTimeDiscretization - Grid object defining the spatial discretization.

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 DiscountCurve riskFreeCurve,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 double jumpIntensity,
 double jumpMean,
 double jumpStdDev,
 double lowerIntegrationBound,
 double upperIntegrationBound,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model without dividend yield curve, using jump parameters.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeCurve - Risk-free discount curve.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpIntensity - Jump intensity.

jumpMean - Mean of the log-jump size.

jumpStdDev - Standard deviation of the log-jump size.

lowerIntegrationBound - Lower integration bound for the log-jump variable.

upperIntegrationBound - Upper integration bound for the log-jump variable.

spaceTimeDiscretization - Grid object defining the spatial discretization.

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 double riskFreeRate,
 double dividendYieldRate,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 BatesJumpComponent jumpComponent,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model from constant rates and an explicit jump component.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeRate - Constant risk-free rate.

dividendYieldRate - Constant dividend yield rate.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpComponent - Bates jump component.

spaceTimeDiscretization - Grid object defining the spatial discretization.

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 double riskFreeRate,
 double dividendYieldRate,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 double jumpIntensity,
 double jumpMean,
 double jumpStdDev,
 double lowerIntegrationBound,
 double upperIntegrationBound,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model from constant rates and jump parameters.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeRate - Constant risk-free rate.

dividendYieldRate - Constant dividend yield rate.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpIntensity - Jump intensity.

jumpMean - Mean of the log-jump size.

jumpStdDev - Standard deviation of the log-jump size.

lowerIntegrationBound - Lower integration bound for the log-jump variable.

upperIntegrationBound - Upper integration bound for the log-jump variable.

spaceTimeDiscretization - Grid object defining the spatial discretization.

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 double riskFreeRate,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 BatesJumpComponent jumpComponent,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model from a constant risk-free rate and zero dividend yield, using an explicit jump component.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeRate - Constant risk-free rate.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpComponent - Bates jump component.

spaceTimeDiscretization - Grid object defining the spatial discretization.

FDMBatesModel

public FDMBatesModel(double initialSpot,
 double initialVariance,
 double riskFreeRate,
 double kappa,
 double thetaV,
 double sigma,
 double rho,
 double jumpIntensity,
 double jumpMean,
 double jumpStdDev,
 double lowerIntegrationBound,
 double upperIntegrationBound,
 SpaceTimeDiscretization spaceTimeDiscretization)

Constructs a Bates finite difference model from a constant risk-free rate and zero dividend yield, using jump parameters.

Parameters:

initialSpot - Initial spot price.

initialVariance - Initial variance.

riskFreeRate - Constant risk-free rate.

kappa - Mean reversion speed of variance.

thetaV - Long-term mean of variance.

sigma - Vol-of-vol parameter.

rho - Correlation between the Brownian motions.

jumpIntensity - Jump intensity.

jumpMean - Mean of the log-jump size.

jumpStdDev - Standard deviation of the log-jump size.

lowerIntegrationBound - Lower integration bound for the log-jump variable.

upperIntegrationBound - Upper integration bound for the log-jump variable.

spaceTimeDiscretization - Grid object defining the spatial discretization.

Method Details

getJumpComponent

public Optional<JumpComponent> getJumpComponent()

Description copied from interface: FiniteDifferenceEquityModel

Returns the optional jump component of the infinitesimal generator.

The default implementation returns Optional.empty(), corresponding to a purely diffusive model.

If present, the returned JumpComponent provides the data needed to assemble the non-local jump part of the generator. The local coefficients returned by FiniteDifferenceEquityModel.getDrift(double, double...) and FiniteDifferenceEquityModel.getFactorLoading(double, double...) keep their current meaning and should remain consistent with the PDE state variables used by the finite-difference discretization.

In particular, under the stock-coordinate convention intended for jump models in this framework, FiniteDifferenceEquityModel.getDrift(double, double...) should continue to return the drift of the local first-order term, while the jump component defines the non-local operator in compensated form.

For a one-dimensional spot variable S, the jump contribution is understood in the form

integral [ f(S exp(y)) - f(S) - S (exp(y) - 1) f'(S) ] nu(dy).

The interpretation of the jump data must remain consistent with the chosen PDE state variables.

Returns:

An Optional containing the jump component of the infinitesimal generator, or Optional.empty() if the model has no jump part.

getBatesJumpComponent

public BatesJumpComponent getBatesJumpComponent()

Returns the Bates jump component.

Returns:

The Bates jump component.

getCloneWithModifiedSpaceTimeDiscretization

public FiniteDifferenceEquityModel getCloneWithModifiedSpaceTimeDiscretization(SpaceTimeDiscretization newSpaceTimeDiscretization)

Description copied from interface: FiniteDifferenceEquityModel

Returns a clone of this model with a modified space-time discretization.

The returned model should represent the same stochastic dynamics and market data as the original one, but on the provided discretization.

Specified by:

getCloneWithModifiedSpaceTimeDiscretization in interface FiniteDifferenceEquityModel

Overrides:

getCloneWithModifiedSpaceTimeDiscretization in class FDMHestonModel

Parameters:

newSpaceTimeDiscretization - The new space-time discretization.

Returns:

A clone of this model with the modified discretization.