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.

翻译：虚构点（又称伪点）允许捕获未位于有限差分离散网格上的边界条件。本文探讨了在扩散方程背景下，虚构点对显式欧拉有限差分格式稳定性的影响。我们特别研究了布莱克-斯科尔斯模型下的一触即付期权情形，但相关观察结果与结论适用于更广泛的金融合约与模型。