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：鬼点（或称虚拟点）允许捕捉未位于有限差分离散化网格上的边界条件。本文研究了在扩散方程背景下，鬼点对显式欧拉有限差分格式稳定性的影响。特别地，我们考虑了Black-Scholes模型下的单触碰期权情形。然而，相关观察结果和结论对于更广泛的金融合约和模型同样适用。