Positive Splitting Method for the Hull & White 2D Black-Scholes Equation

TL;DR

This paper introduces a locally one-dimensional splitting method combined with a finite-volume scheme to efficiently and accurately solve the two-dimensional Hull & White Black-Scholes equation, ensuring non-negativity and handling boundary degeneracy.

Contribution

The paper presents a novel LOD splitting approach with a fitted finite-volume scheme for the 2D Black-Scholes equation, addressing boundary degeneracy and preserving non-negativity.

Findings

Method effectively solves the 2D Hull & White Black-Scholes equation.

Numerical experiments demonstrate high efficiency and accuracy.

The scheme maintains the non-negativity of option prices.

Abstract

In this paper we present a locally one-dimensional (LOD) splitting method to solve numerically the two-dimensional Black-Scholes equation, arising in the Hull & White model for pricing European options with stochastic volatility, characterized by the presence of a mixed derivative term. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite-volume difference scheme, proposed in [23], in order to resolve the degeneration. Discrete maximum principle is proved and therefore our method preserves the non-negativity. Numerical experiments illustrate the efficiency of our difference scheme.