Instabilities of explicit finite difference schemes with ghost points on the diffusion equation
Numerical Analysis
2023-08-22 v2 Numerical Analysis
Computational Finance
Mathematical Finance
Pricing of Securities
Abstract
Ghost, or fictitious points allow to capture boundary conditions that are not located on the finite difference grid discretization. We explore in this paper the impact of ghost points on the stability of the explicit Euler finite difference scheme in the context of the diffusion equation. In particular, we consider the case of a one-touch option under the Black-Scholes model. The observations and results are however valid for a much wider range of financial contracts and models.
Cite
@article{arxiv.2308.04629,
title = {Instabilities of explicit finite difference schemes with ghost points on the diffusion equation},
author = {Fabien Le Floc'h},
journal= {arXiv preprint arXiv:2308.04629},
year = {2023}
}