Document Type: Research Paper
Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran
Classical explicit finite difference schemes are unsuitable for the solution of the famous Black-Scholes partial differential equation, since they impose severe restrictions on the time step. Furthermore, they may produce spurious oscillations in the solution. We propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. The proposed method is constructed based on a nonstandard discretization of the spatial derivatives and is applicable to Black-Scholes equation in the presence of discontinues initial conditions.