Class FDMHestonADI2D
- All Implemented Interfaces:
FDMSolver
Under the Heston model, the state vector is typically given by the spot S and the variance v. The option value u = u(\tau,S,v), written in time-to-maturity coordinates \tau = T - t, satisfies a two-dimensional parabolic PDE of the form
\frac{\partial u}{\partial \tau} = \mathcal{L}_{\mathrm{Heston}} u,
where the Heston generator contains drift terms in both state variables, diffusion terms in both directions, and a mixed derivative induced by the correlation between the Brownian motions driving spot and variance.
This class provides the concrete specialization of AbstractADI2D for
the Heston model. The spatial operator is discretized by the generic
two-dimensional ADI machinery, while the model-specific coefficients are
obtained from FDMHestonModel. The resulting scheme is suitable for
European, Bermudan, and American-style products supported by the surrounding
finite-difference framework.
- Author:
- Alessandro Gnoatto
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Nested Class Summary
Nested classes/interfaces inherited from class AbstractADI2D
AbstractADI2D.DoubleTernaryOperator -
Constructor Summary
ConstructorsConstructorDescriptionFDMHestonADI2D(FDMHestonModel model, FiniteDifferenceEquityProduct product, SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise) Creates the ADI solver for the two-dimensional Heston PDE. -
Method Summary
Methods inherited from class AbstractADI2D
add, applyA0Explicit, applyA1Explicit, applyA2Explicit, applyContinuousObstacleIfNeeded, applyExerciseObstacleIfNeeded, applyFullExplicitOperator, applyInternalConstraints, applyOuterBoundaries, applyProductEventConditionIfNeeded, extractBoundaryValue, flatten, getExercise, getLowerBoundaryValueForFirstDirection, getLowerBoundaryValueForSecondDirection, getModel, getN, getN0, getN1, getProduct, getSpaceTimeDiscretization, getStencilBuilder, getTheta, getUpperBoundaryValueForFirstDirection, getUpperBoundaryValueForSecondDirection, getValue, getValue, getValue, getValues, getValues, getValues, getValuesWithContinuousObstacle, getValueWithContinuousObstacle, getX0Grid, getX1Grid, isInternalConstraintActive, overwriteBoundaryRow, performDouglasHalfStep, performStableDouglasStep, sanitize, scale, solveFirstDirectionLines, solveSecondDirectionLines, subtract
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Constructor Details
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FDMHestonADI2D
public FDMHestonADI2D(FDMHestonModel model, FiniteDifferenceEquityProduct product, SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise) Creates the ADI solver for the two-dimensional Heston PDE.- Parameters:
model- The Heston finite-difference model.product- The product to be valued.spaceTimeDiscretization- The space-time discretization.exercise- The exercise specification.
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