An efficient nonstandard numerical method with positivity preserving property

Document Type: Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran

2 Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran

Abstract

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.

Keywords