Class FDMVarianceGammaModel

java.lang.Object
net.finmath.finitedifference.assetderivativevaluation.models.FDMVarianceGammaModel
All Implemented Interfaces:
FiniteDifferenceBoundary, FiniteDifferenceEquityModel, FiniteDifferenceModel, Model
public class FDMVarianceGammaModel extends Object implements FiniteDifferenceEquityModel
Finite-difference model for option pricing under the Variance Gamma model.

The model is formulated in the stock variable and follows the convention used for jump models in this finite-difference framework:

The public constructors use the usual Variance Gamma parameterization (sigma, nu, theta) in order to stay close to the Monte Carlo side. Constructors / factories based on (C,G,M) are provided only through named static factory methods in order to avoid Java signature clashes.

Author:
Alessandro Gnoatto

  • Constructor Details

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, DiscountCurve riskFreeCurve, DiscountCurve dividendYieldCurve, VarianceGammaJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model from explicit discount curves and an explicit jump component.
      Parameters:
      initialValue - Initial spot value.
      riskFreeCurve - Risk-free discount curve.
      dividendYieldCurve - Dividend yield discount curve.
      jumpComponent - Variance Gamma jump component.
      spaceTimeDiscretization - The space-time discretization.

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, DiscountCurve riskFreeCurve, DiscountCurve dividendYieldCurve, double sigma, double nu, double theta, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model from explicit discount curves and the usual (sigma, nu, theta) parameterization.
      Parameters:
      initialValue - Initial spot value.
      riskFreeCurve - Risk-free discount curve.
      dividendYieldCurve - Dividend yield discount curve.
      sigma - The volatility parameter.
      nu - The variance-of-time-change parameter.
      theta - The asymmetry parameter.
      lowerIntegrationBound - Lower integration bound for the log-jump variable.
      upperIntegrationBound - Upper integration bound for the log-jump variable.
      spaceTimeDiscretization - The space-time discretization.

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, DiscountCurve riskFreeCurve, VarianceGammaJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model assuming zero dividend yield and using an explicit jump component.
      Parameters:
      initialValue - Initial spot value.
      riskFreeCurve - Risk-free discount curve.
      jumpComponent - Variance Gamma jump component.
      spaceTimeDiscretization - The space-time discretization.

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, DiscountCurve riskFreeCurve, double sigma, double nu, double theta, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model assuming zero dividend yield and using the usual (sigma, nu, theta) parameterization.
      Parameters:
      initialValue - Initial spot value.
      riskFreeCurve - Risk-free discount curve.
      sigma - The volatility parameter.
      nu - The variance-of-time-change parameter.
      theta - The asymmetry parameter.
      lowerIntegrationBound - Lower integration bound for the log-jump variable.
      upperIntegrationBound - Upper integration bound for the log-jump variable.
      spaceTimeDiscretization - The space-time discretization.

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, double riskFreeRate, double dividendYieldRate, VarianceGammaJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model from flat rates and an explicit jump component.
      Parameters:
      initialValue - Initial spot value.
      riskFreeRate - Constant risk-free rate.
      dividendYieldRate - Constant dividend yield.
      jumpComponent - Variance Gamma jump component.
      spaceTimeDiscretization - The space-time discretization.

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, double riskFreeRate, double dividendYieldRate, double sigma, double nu, double theta, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model from flat rates and the usual (sigma, nu, theta) parameterization.
      Parameters:
      initialValue - Initial spot value.
      riskFreeRate - Constant risk-free rate.
      dividendYieldRate - Constant dividend yield.
      sigma - The volatility parameter.
      nu - The variance-of-time-change parameter.
      theta - The asymmetry parameter.
      lowerIntegrationBound - Lower integration bound for the log-jump variable.
      upperIntegrationBound - Upper integration bound for the log-jump variable.
      spaceTimeDiscretization - The space-time discretization.

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, double riskFreeRate, VarianceGammaJumpComponent jumpComponent, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model from a flat risk-free rate, assuming zero dividend yield, and using an explicit jump component.
      Parameters:
      initialValue - Initial spot value.
      riskFreeRate - Constant risk-free rate.
      jumpComponent - Variance Gamma jump component.
      spaceTimeDiscretization - The space-time discretization.

    • FDMVarianceGammaModel

      public FDMVarianceGammaModel(double initialValue, double riskFreeRate, double sigma, double nu, double theta, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Creates a Variance Gamma model from a flat risk-free rate, assuming zero dividend yield, and using the usual (sigma, nu, theta) parameterization.
      Parameters:
      initialValue - Initial spot value.
      riskFreeRate - Constant risk-free rate.
      sigma - The volatility parameter.
      nu - The variance-of-time-change parameter.
      theta - The asymmetry parameter.
      lowerIntegrationBound - Lower integration bound for the log-jump variable.
      upperIntegrationBound - Upper integration bound for the log-jump variable.
      spaceTimeDiscretization - The space-time discretization.

  • Method Details

    • ofCGM

      public static FDMVarianceGammaModel ofCGM(double initialValue, DiscountCurve riskFreeCurve, DiscountCurve dividendYieldCurve, double c, double g, double m, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Named factory using the (C,G,M) parameterization and explicit curves.
      Parameters:
      initialValue - Initial spot value.
      riskFreeCurve - Risk-free discount curve.
      dividendYieldCurve - Dividend yield discount curve.
      c - The parameter C.
      g - The parameter G.
      m - The parameter M.
      lowerIntegrationBound - Lower integration bound.
      upperIntegrationBound - Upper integration bound.
      spaceTimeDiscretization - The space-time discretization.
      Returns:
      The corresponding Variance Gamma model.

    • ofCGM

      public static FDMVarianceGammaModel ofCGM(double initialValue, DiscountCurve riskFreeCurve, double c, double g, double m, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Named factory using the (C,G,M) parameterization and zero dividend yield.
      Parameters:
      initialValue - Initial spot value.
      riskFreeCurve - Risk-free discount curve.
      c - The parameter C.
      g - The parameter G.
      m - The parameter M.
      lowerIntegrationBound - Lower integration bound.
      upperIntegrationBound - Upper integration bound.
      spaceTimeDiscretization - The space-time discretization.
      Returns:
      The corresponding Variance Gamma model.

    • ofCGM

      public static FDMVarianceGammaModel ofCGM(double initialValue, double riskFreeRate, double dividendYieldRate, double c, double g, double m, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Named factory using the (C,G,M) parameterization and flat rates.
      Parameters:
      initialValue - Initial spot value.
      riskFreeRate - Constant risk-free rate.
      dividendYieldRate - Constant dividend yield.
      c - The parameter C.
      g - The parameter G.
      m - The parameter M.
      lowerIntegrationBound - Lower integration bound.
      upperIntegrationBound - Upper integration bound.
      spaceTimeDiscretization - The space-time discretization.
      Returns:
      The corresponding Variance Gamma model.

    • ofCGM

      public static FDMVarianceGammaModel ofCGM(double initialValue, double riskFreeRate, double c, double g, double m, double lowerIntegrationBound, double upperIntegrationBound, SpaceTimeDiscretization spaceTimeDiscretization)
      Named factory using the (C,G,M) parameterization, flat risk-free rate, and zero dividend yield.
      Parameters:
      initialValue - Initial spot value.
      riskFreeRate - Constant risk-free rate.
      c - The parameter C.
      g - The parameter G.
      m - The parameter M.
      lowerIntegrationBound - Lower integration bound.
      upperIntegrationBound - Upper integration bound.
      spaceTimeDiscretization - The space-time discretization.
      Returns:
      The corresponding Variance Gamma model.

    • getRiskFreeCurve

      public DiscountCurve getRiskFreeCurve()
      Description copied from interface: FiniteDifferenceEquityModel
      Returns the risk-free discount curve used for pricing.
      Specified by:
      getRiskFreeCurve in interface FiniteDifferenceEquityModel
      Returns:
      The risk-free discount curve.

    • getDividendYieldCurve

      public DiscountCurve getDividendYieldCurve()
      Description copied from interface: FiniteDifferenceEquityModel
      Returns the dividend-yield discount curve.

      This is the legacy single-asset accessor and remains part of the interface to preserve backward compatibility with the current code base.

      For true multi-asset models with one dividend curve per underlying, prefer FiniteDifferenceEquityModel.getDividendYieldCurves(). Such models may override this method with a convention suitable for backward compatibility.

      Specified by:
      getDividendYieldCurve in interface FiniteDifferenceEquityModel
      Returns:
      The dividend-yield discount curve.

    • getInitialValue

      public double[] getInitialValue()
      Description copied from interface: FiniteDifferenceEquityModel
      Returns the initial state vector of the model.

      The returned values must be consistent with the state variables used by the PDE. For example, if the first spatial coordinate is log(S), then the first component should be log(S0) rather than S0.

      Specified by:
      getInitialValue in interface FiniteDifferenceEquityModel
      Returns:
      The initial state vector.

    • getVarianceGammaJumpComponent

      public VarianceGammaJumpComponent getVarianceGammaJumpComponent()
      Returns the value.
      Returns:
      The value.

    • getSpaceTimeDiscretization

      public SpaceTimeDiscretization getSpaceTimeDiscretization()
      Description copied from interface: FiniteDifferenceModel
      Returns the space-time discretization used by this finite difference model.

      The discretization defines the grid in both time and space on which the PDE approximation is constructed.

      Specified by:
      getSpaceTimeDiscretization in interface FiniteDifferenceModel
      Returns:
      The SpaceTimeDiscretization used by this model.

    • getDrift

      public double[] getDrift(double time, double... stateVariables)
      Description copied from interface: FiniteDifferenceEquityModel
      Returns the drift vector of the model state variables.

      The returned coefficients must be expressed in the same coordinates as the PDE state variables used by the finite-difference solver.

      If the state vector is X = (X1, ..., Xn), then this method returns the vector mu(t, X) in

      dX_i(t) = mu_i(t, X_t) dt + ....

      Specified by:
      getDrift in interface FiniteDifferenceEquityModel
      Parameters:
      time - The evaluation time.
      stateVariables - The current values of the model state variables.
      Returns:
      The drift vector.

    • getFactorLoading

      public double[][] getFactorLoading(double time, double... stateVariables)
      Description copied from interface: FiniteDifferenceEquityModel
      Returns the factor-loading matrix of the model state variables.

      The returned coefficients must be expressed in the same coordinates as the PDE state variables used by the finite-difference solver.

      If the state vector is X = (X1, ..., Xn), then this method returns the matrix b(t, X) in

      dX_i(t) = mu_i(t, X_t) dt + sum_j b_{i,j}(t, X_t) dW_j(t).

      Specified by:
      getFactorLoading in interface FiniteDifferenceEquityModel
      Parameters:
      time - The evaluation time.
      stateVariables - The current values of the model state variables.
      Returns:
      The factor-loading matrix.

    • 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.

      Specified by:
      getJumpComponent in interface FiniteDifferenceEquityModel
      Returns:
      An Optional containing the jump component of the infinitesimal generator, or Optional.empty() if the model has no jump part.

    • getBoundaryConditionsAtLowerBoundary

      public BoundaryCondition[] getBoundaryConditionsAtLowerBoundary(FiniteDifferenceEquityProduct product, double time, double... riskFactors)
      Description copied from interface: FiniteDifferenceBoundary
      Returns the boundary conditions at the lower boundary.

      The returned array is indexed by state-variable dimension.

      Specified by:
      getBoundaryConditionsAtLowerBoundary in interface FiniteDifferenceBoundary
      Parameters:
      product - The product being valued.
      time - The running time.
      riskFactors - The state variables specifying the boundary location.
      Returns:
      The lower-boundary conditions by dimension.

    • getBoundaryConditionsAtUpperBoundary

      public BoundaryCondition[] getBoundaryConditionsAtUpperBoundary(FiniteDifferenceEquityProduct product, double time, double... riskFactors)
      Description copied from interface: FiniteDifferenceBoundary
      Returns the boundary conditions at the upper boundary.

      The returned array is indexed by state-variable dimension.

      Specified by:
      getBoundaryConditionsAtUpperBoundary in interface FiniteDifferenceBoundary
      Parameters:
      product - The product being valued.
      time - The running time.
      riskFactors - The state variables specifying the boundary location.
      Returns:
      The upper-boundary conditions by dimension.

    • 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
      Parameters:
      newSpaceTimeDiscretization - The new space-time discretization.
      Returns:
      A clone of this model with the modified discretization.