  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.
