Module net.finmath.lib

Package net.finmath.montecarlo.assetderivativevaluation.models

Class VarianceGammaModel

java.lang.Object

net.finmath.montecarlo.model.AbstractProcessModel

net.finmath.montecarlo.assetderivativevaluation.models.VarianceGammaModel

All Implemented Interfaces:

ProcessModel

public class VarianceGammaModel
extends AbstractProcessModel

This class implements a Variance Gamma Model, that is, it provides the drift and volatility specification and performs the calculation of the numeraire (consistent with the dynamics, i.e. the drift). The model is \[ dS_t = r S dt + S dL, \quad S(0) = S_{0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] where the process L is a VarianceGammaProcess.

Version:

1.0

Author:

Alessandro Gnoatto

See Also:

• The interface for numerical schemes.
• The interface for models provinding parameters to numerical schemes.

Constructor Summary

Constructors

Constructor	Description
VarianceGammaModel(double initialValue, double riskFreeRate, double sigma, double theta, double nu)	Construct a Variance Gamma model with constant rates for the forward price (i.e.
VarianceGammaModel(double initialValue, double riskFreeRate, double discountRate, double sigma, double theta, double nu)	Construct a Variance Gamma model with constant rates for the forward price (i.e.
VarianceGammaModel(double initialValue, DiscountCurve discountCurveForForwardRate, DiscountCurve discountCurveForDiscountRate, double sigma, double theta, double nu)	Construct a Variance Gamma model with discount curves for the forward price (i.e.
VarianceGammaModel(double initialValue, DiscountCurve discountCurveForForwardRate, DiscountCurve discountCurveForDiscountRate, double sigma, double theta, double nu, RandomVariableFactory randomVariableFactory)	Construct a Variance Gamma model with discount curves for the forward price (i.e.
VarianceGammaModel(VarianceGammaModelDescriptor descriptor)	Create the model from a descriptor.
VarianceGammaModel(RandomVariable initialValue, DiscountCurve discountCurveForForwardRate, DiscountCurve discountCurveForDiscountRate, RandomVariable sigma, RandomVariable theta, RandomVariable nu, RandomVariableFactory randomVariableFactory)	Construct a Variance Gamma model with discount curves for the forward price (i.e.
VarianceGammaModel(RandomVariable initialValue, RandomVariable riskFreeRate, RandomVariable discountRate, RandomVariable sigma, RandomVariable theta, RandomVariable nu, RandomVariableFactory randomVariableFactory)	Construct a Variance Gamma model with constant rates for the forward price (i.e.

Method Summary

Modifier and Type	Method	Description
RandomVariable	applyStateSpaceTransform(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)	Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
RandomVariable	applyStateSpaceTransformInverse(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)	Applies the inverse state space transform f-1i to the given random variable such that Xi → f-1i(Xi) =: Yi.
ProcessModel	getCloneWithModifiedData(Map<String,Object> dataModified)	Returns a clone of this model where the specified properties have been modified.
DiscountCurve	getDiscountCurveForDiscountRate()
DiscountCurve	getDiscountCurveForForwardRate()
RandomVariable	getDiscountRate()
RandomVariable[]	getDrift(MonteCarloProcess process, int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)	This method has to be implemented to return the drift, i.e.
RandomVariable[]	getFactorLoading(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex)	This method has to be implemented to return the factor loadings, i.e.
RandomVariable[]	getInitialState(MonteCarloProcess process)	Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.
RandomVariable	getNu()
int	getNumberOfComponents()	Returns the number of components
int	getNumberOfFactors()	Returns the number of factors m, i.e., the number of independent Brownian drivers.
RandomVariable	getNumeraire(MonteCarloProcess process, double time)	Return the numeraire at a given time index.
RandomVariable	getRandomVariableForConstant(double value)	Return a random variable initialized with a constant using the models random variable factory.
RandomVariable	getRiskFreeRate()
RandomVariable	getSigma()
RandomVariable	getTheta()
String	toString()

Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel

getInitialValue, getReferenceDate

Methods inherited from class java.lang.Object

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

Constructor Details

VarianceGammaModel

public VarianceGammaModel(RandomVariable initialValue,
 DiscountCurve discountCurveForForwardRate,
 DiscountCurve discountCurveForDiscountRate,
 RandomVariable sigma,
 RandomVariable theta,
 RandomVariable nu,
 RandomVariableFactory randomVariableFactory)

Construct a Variance Gamma model with discount curves for the forward price (i.e. repo rate minus dividend yield) and for discounting.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate

discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate

sigma - The parameter \( \sigma \).

theta - The parameter \( \theta \).

nu - The parameter \( \nu \).

randomVariableFactory - The factory to be used to construct random variables.

VarianceGammaModel

public VarianceGammaModel(RandomVariable initialValue,
 RandomVariable riskFreeRate,
 RandomVariable discountRate,
 RandomVariable sigma,
 RandomVariable theta,
 RandomVariable nu,
 RandomVariableFactory randomVariableFactory)

Construct a Variance Gamma model with constant rates for the forward price (i.e. repo rate minus dividend yield) and for the discount curve.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

riskFreeRate - The constant risk free rate for the drift (repo rate of the underlying).

discountRate - The constant rate used for discounting.

sigma - The parameter \( \sigma \).

theta - The parameter \( \theta \).

nu - The parameter \( \nu \).

randomVariableFactory - The factory to be used to construct random variables.

VarianceGammaModel

public VarianceGammaModel(VarianceGammaModelDescriptor descriptor)

Create the model from a descriptor.

Parameters:

descriptor - A descriptor of the model.

VarianceGammaModel

public VarianceGammaModel(double initialValue,
 DiscountCurve discountCurveForForwardRate,
 DiscountCurve discountCurveForDiscountRate,
 double sigma,
 double theta,
 double nu,
 RandomVariableFactory randomVariableFactory)

Construct a Variance Gamma model with discount curves for the forward price (i.e. repo rate minus dividend yield) and for discounting.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate

discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate

sigma - The parameter \( \sigma \).

theta - The parameter \( \theta \).

nu - The parameter \( \nu \).

randomVariableFactory - The factory to be used to construct random variables.

VarianceGammaModel

public VarianceGammaModel(double initialValue,
 DiscountCurve discountCurveForForwardRate,
 DiscountCurve discountCurveForDiscountRate,
 double sigma,
 double theta,
 double nu)

Construct a Variance Gamma model with discount curves for the forward price (i.e. repo rate minus dividend yield) and for discounting.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate

discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate

sigma - The parameter \( \sigma \).

theta - The parameter \( \theta \).

nu - The parameter \( \nu \).

VarianceGammaModel

public VarianceGammaModel(double initialValue,
 double riskFreeRate,
 double discountRate,
 double sigma,
 double theta,
 double nu)

Construct a Variance Gamma model with constant rates for the forward price (i.e. repo rate minus dividend yield) and for the discount curve.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

riskFreeRate - The constant risk free rate for the drift (repo rate of the underlying).

discountRate - The constant rate used for discounting.

sigma - The parameter \( \sigma \).

theta - The parameter \( \theta \).

nu - The parameter \( \nu \).

VarianceGammaModel

public VarianceGammaModel(double initialValue,
 double riskFreeRate,
 double sigma,
 double theta,
 double nu)

Construct a Variance Gamma model with constant rates for the forward price (i.e. repo rate minus dividend yield) and for the discount curve.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

riskFreeRate - The constant risk free rate for the drift (repo rate of the underlying).

sigma - The parameter \( \sigma \).

theta - The parameter \( \theta \).

nu - The parameter \( \nu \).

Method Details

applyStateSpaceTransform

public RandomVariable applyStateSpaceTransform(MonteCarloProcess process,
 int timeIndex,
 int componentIndex,
 RandomVariable randomVariable)

Description copied from interface: ProcessModel

Applies the state space transform f_i to the given state random variable such that Y_i → f_i(Y_i) =: X_i.

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

timeIndex - The time index (related to the model times discretization).

componentIndex - The component index i.

randomVariable - The state random variable Y_i.

Returns:

New random variable holding the result of the state space transformation.

applyStateSpaceTransformInverse

public RandomVariable applyStateSpaceTransformInverse(MonteCarloProcess process,
 int timeIndex,
 int componentIndex,
 RandomVariable randomVariable)

Description copied from interface: ProcessModel

Applies the inverse state space transform f^-1_i to the given random variable such that X_i → f^-1_i(X_i) =: Y_i.

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

timeIndex - The time index (related to the model times discretization).

componentIndex - The component index i.

randomVariable - The state random variable X_i.

Returns:

New random variable holding the result of the state space transformation.

getInitialState

public RandomVariable[] getInitialState(MonteCarloProcess process)

Description copied from interface: ProcessModel

Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

Returns:

The initial value of the state variable of the process Y(t=0).

getNumeraire

public RandomVariable getNumeraire(MonteCarloProcess process,
 double time)

Description copied from interface: ProcessModel

Return the numeraire at a given time index. Note: The random variable returned is a defensive copy and may be modified.

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

time - The time t for which the numeraire N(t) should be returned.

Returns:

The numeraire at the specified time as RandomVariable

getDrift

public RandomVariable[] getDrift(MonteCarloProcess process,
 int timeIndex,
 RandomVariable[] realizationAtTimeIndex,
 RandomVariable[] realizationPredictor)

Description copied from interface: ProcessModel

This method has to be implemented to return the drift, i.e. the coefficient vector
μ = (μ₁, ..., μ_n) such that X = f(Y) and
dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m
in an m-factor model. Here j denotes index of the component of the resulting process. Since the model is provided only on a time discretization, the method may also (should try to) return the drift as \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \).

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

timeIndex - The time index (related to the model times discretization).

realizationAtTimeIndex - The given realization at timeIndex

realizationPredictor - The given realization at timeIndex+1 or null if no predictor is available.

Returns:

The drift or average drift from timeIndex to timeIndex+1, i.e. \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \) (or a suitable approximation).

getFactorLoading

public RandomVariable[] getFactorLoading(MonteCarloProcess process,
 int timeIndex,
 int componentIndex,
 RandomVariable[] realizationAtTimeIndex)

Description copied from interface: ProcessModel

This method has to be implemented to return the factor loadings, i.e. the coefficient vector
λ_j = (λ_1,j, ..., λ_m,j) such that X = f(Y) and
dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m
in an m-factor model. Here j denotes index of the component of the resulting process.

Parameters:

process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.

timeIndex - The time index (related to the model times discretization).

componentIndex - The index j of the driven component.

realizationAtTimeIndex - The realization of X at the time corresponding to timeIndex (in order to implement local and stochastic volatlity models).

Returns:

The factor loading for given factor and component.

getNumberOfComponents

public int getNumberOfComponents()

Description copied from interface: ProcessModel

Returns the number of components

Returns:

The number of components

getNumberOfFactors

public int getNumberOfFactors()

Description copied from interface: ProcessModel

Returns the number of factors m, i.e., the number of independent Brownian drivers.

Returns:

The number of factors.

getRandomVariableForConstant

public RandomVariable getRandomVariableForConstant(double value)

Description copied from interface: ProcessModel

Return a random variable initialized with a constant using the models random variable factory.

Parameters:

value - The constant value.

Returns:

A new random variable initialized with a constant value.

getCloneWithModifiedData

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

Description copied from interface: ProcessModel

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.

Parameters:

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

Returns:

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

Throws:

CalculationException - Thrown when the model could not be created.

getDiscountCurveForForwardRate

public DiscountCurve getDiscountCurveForForwardRate()

Returns:

the discountCurveForForwardRate

getRiskFreeRate

public RandomVariable getRiskFreeRate()

Returns:

the riskFreeRate

getDiscountCurveForDiscountRate

public DiscountCurve getDiscountCurveForDiscountRate()

Returns:

the discountCurveForDiscountRate

getDiscountRate

public RandomVariable getDiscountRate()

Returns:

the discountRate

getSigma

public RandomVariable getSigma()

Returns:

the sigma

getTheta

public RandomVariable getTheta()

Returns:

the theta

getNu

public RandomVariable getNu()

Returns:

the nu

toString

public String toString()

Overrides:

toString in class Object