Class FDMThetaMethod1DJump

java.lang.Object
net.finmath.finitedifference.solvers.FDMThetaMethod1DJump
All Implemented Interfaces:
FDMSolver
public class FDMThetaMethod1DJump extends Object implements FDMSolver
Theta-method solver for a one-dimensional PIDE with an explicit jump term.

The local diffusive part is handled through the usual theta-method discretization, leading to a tridiagonal linear system at each time step. The non-local jump contribution is treated explicitly and is therefore added to the right-hand side in IMEX form.

For a one-dimensional state variable x, the jump term is interpreted as 

integral [ u(x exp(y)) - u(x) - x (exp(y) - 1) u_x(x) ] nu(dy),

where y denotes the log-relative jump size.

The numerical quadrature splits the integration interval at zero in order to avoid sampling the Levy density exactly at the singular point. This makes the implementation suitable not only for finite-activity jump models such as Merton, but also for infinite-activity models such as Variance Gamma, provided the jump component supplies a finite numerical integration window.

Current scope:

  • one-dimensional space grids only,
  • jumps acting on state variable index 0,
  • explicit treatment of the jump operator,
  • linear interpolation with constant extrapolation for shifted values.
Author:
Alessandro Gnoatto

  • Constructor Summary

    Constructors
    Constructor
    Description
    FDMThetaMethod1DJump(net.finmath.finitedifference.assetderivativevaluation.models.FiniteDifferenceEquityModel model, net.finmath.finitedifference.assetderivativevaluation.products.FiniteDifferenceEquityProduct product, net.finmath.finitedifference.grids.SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise)
    Creates a one-dimensional theta-method PIDE solver with explicit jump term.
    FDMThetaMethod1DJump(net.finmath.finitedifference.assetderivativevaluation.models.FiniteDifferenceEquityModel model, net.finmath.finitedifference.assetderivativevaluation.products.FiniteDifferenceEquityProduct product, net.finmath.finitedifference.grids.SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise, int quadraturePointsPerSide)
    Creates a one-dimensional theta-method PIDE solver with explicit jump term.

  • Method Summary

    Modifier and Type
    Method
    Description
    double[]
    getValue(double evaluationTime, double time, double[] terminalValues)
    Returns the solution at a given evaluation time for terminal values already sampled on the spatial grid.
    double[]
    getValue(double evaluationTime, double time, double[] terminalValues, DoubleBinaryOperator continuousObstacleValue)
    Returns the solution at a given evaluation time for a problem with a continuous obstacle.
    double[]
    getValue(double evaluationTime, double time, double[] terminalValues, DoubleUnaryOperator exerciseValue)
    Returns the solution at a given evaluation time for a product with discrete early exercise opportunities.
    double[]
    getValue(double evaluationTime, double time, DoubleUnaryOperator valueAtMaturity)
    Returns the solution at a given evaluation time for a payoff specified as a terminal value function.
    double[][]
    getValues(double time, double[] terminalValues)
    Returns the full space-time solution for terminal values already sampled on the spatial grid.
    double[][]
    getValues(double time, double[] terminalValues, DoubleBinaryOperator continuousObstacleValue)
    Returns the full space-time solution for a problem with a continuous obstacle.
    double[][]
    getValues(double time, double[] terminalValues, DoubleUnaryOperator exerciseValue)
    Returns the full space-time solution for a product with discrete early exercise opportunities.
    double[][]
    getValues(double time, DoubleUnaryOperator valueAtMaturity)
    Returns the full space-time solution for a payoff specified as a terminal value function.

    Methods inherited from class Object

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

    Methods inherited from interface FDMSolver

    getValue, getValues

  • Constructor Details

    • FDMThetaMethod1DJump

      public FDMThetaMethod1DJump(net.finmath.finitedifference.assetderivativevaluation.models.FiniteDifferenceEquityModel model, net.finmath.finitedifference.assetderivativevaluation.products.FiniteDifferenceEquityProduct product, net.finmath.finitedifference.grids.SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise)
      Creates a one-dimensional theta-method PIDE solver with explicit jump term.

      This constructor uses a default number of quadrature cells on each side of zero for the evaluation of the jump integral.

      Parameters:
      model - The finite-difference model.
      product - The product to be valued.
      spaceTimeDiscretization - The space-time discretization.
      exercise - The exercise specification.

    • FDMThetaMethod1DJump

      public FDMThetaMethod1DJump(net.finmath.finitedifference.assetderivativevaluation.models.FiniteDifferenceEquityModel model, net.finmath.finitedifference.assetderivativevaluation.products.FiniteDifferenceEquityProduct product, net.finmath.finitedifference.grids.SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise, int quadraturePointsPerSide)
      Creates a one-dimensional theta-method PIDE solver with explicit jump term.

      The local operator is handled implicitly through the theta method, while the jump contribution is evaluated explicitly by numerical quadrature.

      Parameters:
      model - The finite-difference model.
      product - The product to be valued.
      spaceTimeDiscretization - The space-time discretization.
      exercise - The exercise specification.
      quadraturePointsPerSide - Number of quadrature cells used on each side of zero for the numerical evaluation of the jump integral.

  • Method Details

    • getValues

      public double[][] getValues(double time, DoubleUnaryOperator valueAtMaturity)
      Returns the full space-time solution for a payoff specified as a terminal value function.

      The payoff is sampled on the spatial grid at maturity and then propagated backwards in time.

      Specified by:
      getValues in interface FDMSolver
      Parameters:
      time - The maturity time.
      valueAtMaturity - The terminal payoff function.
      Returns:
      The full space-time solution matrix.

    • getValue

      public double[] getValue(double evaluationTime, double time, DoubleUnaryOperator valueAtMaturity)
      Returns the solution at a given evaluation time for a payoff specified as a terminal value function.
      Specified by:
      getValue in interface FDMSolver
      Parameters:
      evaluationTime - The time at which the solution is requested.
      time - The maturity time.
      valueAtMaturity - The terminal payoff function.
      Returns:
      The solution vector on the spatial grid at the requested time.

    • getValues

      public double[][] getValues(double time, double[] terminalValues)
      Returns the full space-time solution for terminal values already sampled on the spatial grid.
      Specified by:
      getValues in interface FDMSolver
      Parameters:
      time - The maturity time.
      terminalValues - The terminal values on the spatial grid.
      Returns:
      The full space-time solution matrix.

    • getValue

      public double[] getValue(double evaluationTime, double time, double[] terminalValues)
      Returns the solution at a given evaluation time for terminal values already sampled on the spatial grid.
      Specified by:
      getValue in interface FDMSolver
      Parameters:
      evaluationTime - The time at which the solution is requested.
      time - The maturity time.
      terminalValues - The terminal values on the spatial grid.
      Returns:
      The solution vector on the spatial grid at the requested time.

    • getValues

      public double[][] getValues(double time, double[] terminalValues, DoubleUnaryOperator exerciseValue)
      Returns the full space-time solution for a product with discrete early exercise opportunities.
      Specified by:
      getValues in interface FDMSolver
      Parameters:
      time - The maturity time.
      terminalValues - The terminal values on the spatial grid.
      exerciseValue - The pointwise exercise value.
      Returns:
      The full space-time solution matrix.

    • getValue

      public double[] getValue(double evaluationTime, double time, double[] terminalValues, DoubleUnaryOperator exerciseValue)
      Returns the solution at a given evaluation time for a product with discrete early exercise opportunities.
      Specified by:
      getValue in interface FDMSolver
      Parameters:
      evaluationTime - The time at which the solution is requested.
      time - The maturity time.
      terminalValues - The terminal values on the spatial grid.
      exerciseValue - The pointwise exercise value.
      Returns:
      The solution vector on the spatial grid at the requested time.

    • getValues

      public double[][] getValues(double time, double[] terminalValues, DoubleBinaryOperator continuousObstacleValue)
      Returns the full space-time solution for a problem with a continuous obstacle.
      Parameters:
      time - The maturity time.
      terminalValues - The terminal values on the spatial grid.
      continuousObstacleValue - The obstacle as a function of time and state.
      Returns:
      The full space-time solution matrix.

    • getValue

      public double[] getValue(double evaluationTime, double time, double[] terminalValues, DoubleBinaryOperator continuousObstacleValue)
      Returns the solution at a given evaluation time for a problem with a continuous obstacle.
      Parameters:
      evaluationTime - The time at which the solution is requested.
      time - The maturity time.
      terminalValues - The terminal values on the spatial grid.
      continuousObstacleValue - The obstacle as a function of time and state.
      Returns:
      The solution vector on the spatial grid at the requested time.