Class FDMHestonModel

java.lang.Object
net.finmath.finitedifference.assetderivativevaluation.models.FDMHestonModel
All Implemented Interfaces:
FiniteDifferenceBoundary, FiniteDifferenceEquityModel, FiniteDifferenceModel, Model
Direct Known Subclasses:
FDMBatesModel
public class FDMHestonModel extends Object implements FiniteDifferenceEquityModel
Finite difference model for option pricing under the Heston stochastic volatility model.

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

The methods getDrift(double, double...) and getFactorLoading(double, double...) follow the conventions used in FiniteDifferenceEquityModel:

  • getDrift returns the vector of drifts for the state variables.
  • getFactorLoading returns the matrix of factor loadings (here 2 factors), producing the correct covariance with correlation rho.

Boundary conditions are provided through the FiniteDifferenceBoundary interface methods, via FDBoundaryFactory.

Author:
Alessandro Gnoatto, Enrico De Vecchi

  • Constructor Details

    • FDMHestonModel

      public FDMHestonModel(double initialSpot, double initialVariance, DiscountCurve riskFreeCurve, DiscountCurve dividendYieldCurve, double kappa, double thetaV, double sigma, double rho, SpaceTimeDiscretization spaceTimeDiscretization)
      Constructs a Heston finite difference model for option pricing.
      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 spot and variance Brownian motions.
      spaceTimeDiscretization - Grid object defining the spatial discretization.

    • FDMHestonModel

      public FDMHestonModel(double initialSpot, double initialVariance, DiscountCurve riskFreeCurve, double kappa, double thetaV, double sigma, double rho, SpaceTimeDiscretization spaceTimeDiscretization)
      Constructs a Heston finite difference model for option pricing without dividend yield curve (i.e. dividend yield is assumed to be zero).
      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 spot and variance Brownian motions.
      spaceTimeDiscretization - Grid object defining the spatial discretization.

    • FDMHestonModel

      public FDMHestonModel(double initialSpot, double initialVariance, double riskFreeRate, double dividendYieldRate, double kappa, double thetaV, double sigma, double rho, SpaceTimeDiscretization spaceTimeDiscretization)
      Constructs a Heston finite difference model for option pricing from constant rates.
      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 spot and variance Brownian motions.
      spaceTimeDiscretization - Grid object defining the spatial discretization.

    • FDMHestonModel

      public FDMHestonModel(double initialSpot, double initialVariance, double riskFreeRate, double kappa, double thetaV, double sigma, double rho, SpaceTimeDiscretization spaceTimeDiscretization)
      Constructs a Heston finite difference model for option pricing from a constant risk-free rate and zero dividend yield.
      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 spot and variance Brownian motions.
      spaceTimeDiscretization - Grid object defining the spatial discretization.

  • Method Details

    • 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()
      Returns the initial value of the system of SDEs.
      Specified by:
      getInitialValue in interface FiniteDifferenceEquityModel
      Returns:
      The initial spot.

    • getKappa

      public double getKappa()
      Returns the mean reversion speed of variance.
      Returns:
      The parameter kappa.

    • getThetaV

      public double getThetaV()
      Returns the long-term mean of variance.
      Returns:
      The parameter thetaV.

    • getSigma

      public double getSigma()
      Returns the vol-of-vol parameter.
      Returns:
      The parameter sigma.

    • getRho

      public double getRho()
      Returns the correlation between the Brownian motions.
      Returns:
      The parameter rho.

    • 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.

    • getCovariance

      public double[][] getCovariance(double time, double... stateVariables)
      Convenience method returning the covariance matrix a = B B^T, derived from getFactorLoading(double, double...).
      Parameters:
      time - Evaluation time.
      stateVariables - State variables.
      Returns:
      The covariance matrix.

    • 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.