Class BarrierAlignedSpotGridFactory

java.lang.Object

net.finmath.finitedifference.grids.BarrierAlignedSpotGridFactory

public final class BarrierAlignedSpotGridFactory
extends Object

Utility factory for spot grids used in barrier option PDE problems.

Main features:

• forces the barrier to be an exact grid node,
• can build either a uniform or a clustered grid,
• clustered grid puts more points near the barrier.

The clustered grid is piecewise-defined: on each side of the barrier, nodes are generated with a power transform. For clusteringExponent > 1.0, points concentrate near the barrier. For clusteringExponent = 1.0, the grid is piecewise uniform.

This class is intended especially for direct barrier pricing under Heston/SABR, where barrier alignment can materially improve knock-in accuracy.

Author:

Alessandro Gnoatto

Method Summary

Modifier and Type	Method	Description
static Grid	createBarrierAlignedClusteredGrid(int numberOfSteps, double sMin, double sMax, double barrier, double clusteringExponent)	Creates a barrier-aligned clustered grid.
static Grid	createBarrierAlignedUniformGrid(int numberOfSteps, double sMin, double sMax, double barrier)	Creates a uniform grid with the barrier exactly on a node.
static int	findBarrierIndex(double[] grid, double barrier)	Returns the index of the barrier node in a grid previously built by this factory.
static int	findBarrierIndex(Grid grid, double barrier)	Convenience overload.

Methods inherited from class Object

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

Method Details

createBarrierAlignedUniformGrid

public static Grid createBarrierAlignedUniformGrid(int numberOfSteps,
 double sMin,
 double sMax,
 double barrier)

Creates a uniform grid with the barrier exactly on a node.

The spacing is chosen so that:

• the barrier lies exactly on a node,
• the lower/upper bounds are preserved,
• the number of intervals is exactly numberOfSteps.

This method requires the barrier to lie strictly inside the interval.

Parameters:

numberOfSteps - Number of grid intervals.

sMin - Lower grid boundary.

sMax - Upper grid boundary.

barrier - Barrier level.

Returns:

A grid with the barrier exactly on a node.

createBarrierAlignedClusteredGrid

public static Grid createBarrierAlignedClusteredGrid(int numberOfSteps,
 double sMin,
 double sMax,
 double barrier,
 double clusteringExponent)

Creates a barrier-aligned clustered grid.

The barrier is exactly on a node. Points are concentrated near the barrier using a power transform on each side:

x = barrier - (barrier - sMin) * (1 - u)^p    on the left side
x = barrier + (sMax - barrier) * u^p          on the right side

where p = clusteringExponent.

• clusteringExponent = 1.0: piecewise uniform
• clusteringExponent > 1.0: points cluster near the barrier

Parameters:

numberOfSteps - Number of grid intervals.

sMin - Lower grid boundary.

sMax - Upper grid boundary.

barrier - Barrier level.

clusteringExponent - Clustering strength, must be >= 1.0.

Returns:

A clustered grid with the barrier exactly on a node.

findBarrierIndex

public static int findBarrierIndex(double[] grid,
 double barrier)

Returns the index of the barrier node in a grid previously built by this factory.

Parameters:

grid - The grid array.

barrier - The barrier level.

Returns:

The barrier node index.

findBarrierIndex

public static int findBarrierIndex(Grid grid,
 double barrier)

Convenience overload.

Parameters:

grid - The grid.

barrier - The barrier level.

Returns:

The barrier node index.