finMath lib documentation
net.finmath.montecarlo.assetderivativevaluation.models

## Class VarianceGammaModel

• ### Constructor Summary

Constructors
Constructor and Description
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.
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.
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.
• ### Method Summary

All Methods
Modifier and Type Method and Description
RandomVariable applyStateSpaceTransform(int componentIndex, RandomVariable randomVariable)
Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
RandomVariable applyStateSpaceTransformInverse(int componentIndex, RandomVariable randomVariable)
ProcessModel getCloneWithModifiedData(Map<String,Object> dataModified)
Returns a clone of this model where the specified properties have been modified.
DiscountCurve getDiscountCurveForDiscountRate()
DiscountCurve getDiscountCurveForForwardRate()
double getDiscountRate()
RandomVariable[] getDrift(int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)
This method has to be implemented to return the drift, i.e.
RandomVariable[] getFactorLoading(int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex)
This method has to be implemented to return the factor loadings, i.e.
RandomVariable[] getInitialState()
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.
double getNu()
int getNumberOfComponents()
Returns the number of components
RandomVariable getNumeraire(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.
double getRiskFreeRate()
double getSigma()
double getTheta()
String toString()
• ### Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel

getInitialValue, getMonteCarloWeights, getNumberOfFactors, getProcess, getProcessValue, getReferenceDate, getTime, getTimeDiscretization, getTimeIndex, setProcess
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
• ### Constructor Detail

• #### 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 Detail

• #### getNumberOfComponents

public int getNumberOfComponents()
Description copied from interface: ProcessModel
Returns the number of components
Returns:
The number of components
• #### applyStateSpaceTransform

public RandomVariable applyStateSpaceTransform(int componentIndex,
RandomVariable randomVariable)
Description copied from interface: ProcessModel
Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
Parameters:
componentIndex - The component index i.
randomVariable - The state random variable Yi.
Returns:
New random variable holding the result of the state space transformation.
• #### applyStateSpaceTransformInverse

public RandomVariable applyStateSpaceTransformInverse(int componentIndex,
RandomVariable randomVariable)
• #### getInitialState

public RandomVariable[] getInitialState()
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.
Returns:
The initial value of the state variable of the process Y(t=0).
• #### getNumeraire

public RandomVariable getNumeraire(double time)
throws CalculationException
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:
time - The time t for which the numeraire N(t) should be returned.
Returns:
The numeraire at the specified time as RandomVariableFromDoubleArray
Throws:
CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.
• #### getDrift

public RandomVariable[] getDrift(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, ..., μn) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
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:
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).

public RandomVariable[] getFactorLoading(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
λj = (λ1,j, ..., λm,j) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
in an m-factor model. Here j denotes index of the component of the resulting process.
Parameters:
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:
• #### 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 double getRiskFreeRate()
Returns:
the riskFreeRate
• #### getDiscountCurveForDiscountRate

public DiscountCurve getDiscountCurveForDiscountRate()
Returns:
the discountCurveForDiscountRate
• #### getDiscountRate

public double getDiscountRate()
Returns:
the discountRate
• #### getSigma

public double getSigma()
Returns:
the sigma
• #### getTheta

public double getTheta()
Returns:
the theta
• #### getNu

public double getNu()
Returns:
the nu
• #### toString

public String toString()
Overrides:
toString in class Object