Class FDMAsianHestonADI3D

java.lang.Object

net.finmath.finitedifference.solvers.adi.AbstractADI3D

net.finmath.finitedifference.solvers.adi.FDMAsianHestonADI3D

All Implemented Interfaces:

FDMSolver

public class FDMAsianHestonADI3D
extends AbstractADI3D

Specialized 3D ADI solver for arithmetic Asian options under a lifted Heston state (S, v, I), where dS_t = mu_S dt + diffusion terms, dv_t = mu_v dt + diffusion terms, dI_t = S_t dt. In time-to-maturity tau = T - t, the backward pricing PDE is split as u_tau = A0 u + A1 u + A2 u + A3 u with A0: discount term and mixed derivative terms (treated explicitly) A1: S-direction drift and diffusion (treated implicitly) A2: v-direction drift and diffusion (treated implicitly) A3: I-direction transport S * u_I (treated with a specialized implicit upwind solve) There is: - no diffusion in the I direction - no mixed derivative involving I The I direction is pure transport. In tau-time, the correct upwind discretization is forward in I.

Author:

Alessandro Gnoatto

Nested Class Summary

Nested classes/interfaces inherited from class AbstractADI3D

AbstractADI3D.DoubleQuaternaryOperator, AbstractADI3D.DoubleTernaryOperator

Constructor Summary

Constructors

Constructor	Description
FDMAsianHestonADI3D(FiniteDifferenceEquityModel model, FiniteDifferenceEquityProduct product, SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise)	Performs the operation.

Method Summary

Modifier and Type	Method	Description
protected double[]	applyA3Explicit(double[] u, double time)	Explicit application of A3 u = S * u_I using forward upwinding in I: u_I(S_i, v_j, I_k) ~ (u_{i,j,k+1} - u_{i,j,k}) / (I_{k+1} - I_k) for k = 0,...,n2-2.
protected double[]	solveFirstDirectionLines(double[] rhs, double time, double dt)
protected double[]	solveSecondDirectionLines(double[] rhs, double time, double dt)
protected double[]	solveThirdDirectionLines(double[] rhs, double time, double dt)

Methods inherited from class AbstractADI3D

add, applyA0Explicit, applyA1Explicit, applyA2Explicit, applyExerciseObstacleIfNeeded, applyFullExplicitOperator, applyInternalConstraints, applyOuterBoundaries, extractBoundaryValue, flatten, getExercise, getLowerBoundaryValueForFirstDirection, getLowerBoundaryValueForSecondDirection, getLowerBoundaryValueForThirdDirection, getModel, getN, getN0, getN1, getN2, getProduct, getSpaceTimeDiscretization, getTheta, getUpperBoundaryValueForFirstDirection, getUpperBoundaryValueForSecondDirection, getUpperBoundaryValueForThirdDirection, getValue, getValue, getValue, getValue, getValues, getValues, getValues, getValues, getX0Grid, getX1Grid, getX2Grid, isInternalConstraintActive, overwriteBoundaryRow, performDouglasHalfStep, performStableDouglasStep, sanitize, scale, subtract

Methods inherited from class Object

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

Methods inherited from interface FDMSolver

getValue, getValue, getValues, getValues

Constructor Details

FDMAsianHestonADI3D

public FDMAsianHestonADI3D(FiniteDifferenceEquityModel model,
 FiniteDifferenceEquityProduct product,
 SpaceTimeDiscretization spaceTimeDiscretization,
 Exercise exercise)

Performs the operation.

Parameters:

model - The value.

product - The value.

spaceTimeDiscretization - The value.

exercise - The value.

Method Details

applyA3Explicit

protected double[] applyA3Explicit(double[] u,
 double time)

Explicit application of A3 u = S * u_I using forward upwinding in I: u_I(S_i, v_j, I_k) ~ (u_{i,j,k+1} - u_{i,j,k}) / (I_{k+1} - I_k) for k = 0,...,n2-2. The top I-row k = n2 - 1 is handled via the upper I boundary.

Overrides:

applyA3Explicit in class AbstractADI3D

solveFirstDirectionLines

protected double[] solveFirstDirectionLines(double[] rhs,
 double time,
 double dt)

Specified by:

solveFirstDirectionLines in class AbstractADI3D

solveSecondDirectionLines

protected double[] solveSecondDirectionLines(double[] rhs,
 double time,
 double dt)

Specified by:

solveSecondDirectionLines in class AbstractADI3D

solveThirdDirectionLines

protected double[] solveThirdDirectionLines(double[] rhs,
 double time,
 double dt)

Specified by:

solveThirdDirectionLines in class AbstractADI3D