Class FDMBarrierSabrADI2D

java.lang.Object

net.finmath.finitedifference.solvers.adi.AbstractADI2D

net.finmath.finitedifference.solvers.adi.FDMBarrierSabrADI2D

All Implemented Interfaces:

FDMSolver

public class FDMBarrierSabrADI2D
extends AbstractADI2D

Barrier-aware ADI finite difference solver for the two-dimensional SABR PDE.

This class supports:

• standard direct barrier solves via BarrierPDEMode.OUT_STANDARD,
• pre-hit continuation solves for direct knock-in pricing via BarrierPDEMode.IN_PRE_HIT.

In pre-hit mode, the barrier is treated as an interface on the first state variable and the activated post-hit value is injected through an ActivatedBarrierTrace2D. The exercise obstacle is intentionally disabled in that mode.

Author:

Alessandro Gnoatto

Nested Class Summary

Nested classes/interfaces inherited from class AbstractADI2D

AbstractADI2D.DoubleTernaryOperator

Constructor Summary

Constructors

Constructor	Description
FDMBarrierSabrADI2D(FDMSabrModel model, FiniteDifferenceEquityProduct product, SpaceTimeDiscretization spaceTimeDiscretization, Exercise exercise, BarrierPDEMode barrierMode, BarrierPreHitSpecification preHitSpecification)	Creates the barrier-aware SABR ADI solver.

Method Summary

Modifier and Type	Method	Description
protected void	applyBarrierTraceIfNeeded(double runningTime, double[] u)	Applies the barrier trace directly to the flattened solution vector.
protected void	applyOuterBoundaries(double time, double[] u)
BarrierPDEMode	getBarrierMode()	Returns the barrier PDE mode.
protected double	getBarrierTraceValue(int secondIndex, double runningTime)	Returns the activated barrier trace value at the given second-state row and running time.
BarrierPreHitSpecification	getPreHitSpecification()	Returns the pre-hit specification, or null if not in pre-hit mode.
FDMSabrModel	getSabrModel()	Returns the SABR model used by this solver.
double[][]	getValues(double time, DoubleBinaryOperator valueAtMaturity)	Returns the full value surface for a two-dimensional terminal payoff.
double[][]	getValues(double time, DoubleBinaryOperator valueAtMaturity, AbstractADI2D.DoubleTernaryOperator exerciseValue)	Returns the full value surface under a discrete exercise obstacle.
double[][]	getValues(double time, DoubleUnaryOperator valueAtMaturity)	Returns the full value surface for a terminal payoff depending on the first state variable.
protected boolean	isPreHitMode()	Returns true if this solver is in pre-hit continuation mode.
protected void	overwriteBarrierTraceRow(TridiagonalMatrix matrix, double[] rhs, int secondIndex, double runningTime)	Overwrites the barrier interface row in a first-direction tridiagonal system.
protected double[]	solveFirstDirectionLines(double[] rhs, double time, double dt)

Methods inherited from class AbstractADI2D

add, applyA0Explicit, applyA1Explicit, applyA2Explicit, applyContinuousObstacleIfNeeded, applyExerciseObstacleIfNeeded, applyFullExplicitOperator, applyInternalConstraints, applyProductEventConditionIfNeeded, extractBoundaryValue, flatten, getExercise, getLowerBoundaryValueForFirstDirection, getLowerBoundaryValueForSecondDirection, getModel, getN, getN0, getN1, getProduct, getSpaceTimeDiscretization, getStencilBuilder, getTheta, getUpperBoundaryValueForFirstDirection, getUpperBoundaryValueForSecondDirection, getValue, getValue, getValue, getValuesWithContinuousObstacle, getValueWithContinuousObstacle, getX0Grid, getX1Grid, isInternalConstraintActive, overwriteBoundaryRow, performDouglasHalfStep, performStableDouglasStep, sanitize, scale, solveSecondDirectionLines, 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

FDMBarrierSabrADI2D

public FDMBarrierSabrADI2D(FDMSabrModel model,
 FiniteDifferenceEquityProduct product,
 SpaceTimeDiscretization spaceTimeDiscretization,
 Exercise exercise,
 BarrierPDEMode barrierMode,
 BarrierPreHitSpecification preHitSpecification)

Creates the barrier-aware SABR ADI solver.

Parameters:

model - The SABR model.

product - The finite-difference product.

spaceTimeDiscretization - The discretization to use.

exercise - The exercise specification.

barrierMode - The barrier PDE mode.

preHitSpecification - The pre-hit specification. Required in IN_PRE_HIT mode.

Method Details

getValues

public double[][] getValues(double time,
 DoubleUnaryOperator valueAtMaturity)

Description copied from class: AbstractADI2D

Returns the full value surface for a terminal payoff depending on the first state variable.

Specified by:

getValues in interface FDMSolver

Overrides:

getValues in class AbstractADI2D

Parameters:

time - Maturity time.

valueAtMaturity - Terminal payoff.

Returns:

Value surface indexed by flattened space index and time index.

getValues

public double[][] getValues(double time,
 DoubleBinaryOperator valueAtMaturity)

Description copied from class: AbstractADI2D

Returns the full value surface for a two-dimensional terminal payoff.

Specified by:

getValues in interface FDMSolver

Overrides:

getValues in class AbstractADI2D

Parameters:

time - Maturity time.

valueAtMaturity - Terminal payoff.

Returns:

Value surface indexed by flattened space index and time index.

getValues

public double[][] getValues(double time,
 DoubleBinaryOperator valueAtMaturity,
 AbstractADI2D.DoubleTernaryOperator exerciseValue)

Description copied from class: AbstractADI2D

Returns the full value surface under a discrete exercise obstacle.

Overrides:

getValues in class AbstractADI2D

Parameters:

time - Maturity time.

valueAtMaturity - Terminal payoff.

exerciseValue - Exercise payoff.

Returns:

Value surface indexed by flattened space index and time index.

solveFirstDirectionLines

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

Overrides:

solveFirstDirectionLines in class AbstractADI2D

applyOuterBoundaries

protected void applyOuterBoundaries(double time,
 double[] u)

Overrides:

applyOuterBoundaries in class AbstractADI2D

isPreHitMode

protected boolean isPreHitMode()

Returns true if this solver is in pre-hit continuation mode.

Returns:

True if in pre-hit mode.

overwriteBarrierTraceRow

protected void overwriteBarrierTraceRow(TridiagonalMatrix matrix,
 double[] rhs,
 int secondIndex,
 double runningTime)

Overwrites the barrier interface row in a first-direction tridiagonal system.

Parameters:

matrix - The tridiagonal matrix.

rhs - The corresponding right-hand side.

secondIndex - The second-state index.

runningTime - The running time.

applyBarrierTraceIfNeeded

protected void applyBarrierTraceIfNeeded(double runningTime,
 double[] u)

Applies the barrier trace directly to the flattened solution vector.

Parameters:

runningTime - The running time.

u - The solution vector.

getBarrierTraceValue

protected double getBarrierTraceValue(int secondIndex,
 double runningTime)

Returns the activated barrier trace value at the given second-state row and running time.

Parameters:

secondIndex - The second-state index.

runningTime - The running time.

Returns:

The corresponding trace value.

getSabrModel

public FDMSabrModel getSabrModel()

Returns the SABR model used by this solver.

Returns:

The SABR model.

getBarrierMode

public BarrierPDEMode getBarrierMode()

Returns the barrier PDE mode.

Returns:

The barrier mode.

getPreHitSpecification

public BarrierPreHitSpecification getPreHitSpecification()

Returns the pre-hit specification, or null if not in pre-hit mode.

Returns:

The pre-hit specification.