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In this paper we propose an explicit finite-difference scheme to solve the American option pricing problem. It is based on front-fixing transformation that involves unknown free boundary to the equation. The proposed stable and consistent numerical scheme preserves positivity and monotonicity of the solution in accordance with the behavior of the exact solution. Numerical examples and comparison with other methods are included. This technique can be applied to some types of two-asset options after reducing the dimension. In the paper the front-fixing method is applied to exchange option pricing.

[EN] This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. Taking advantage of a cross derivative removing technique, an explicit difference scheme is developed retaining the benefits of the one-dimensional finite difference method, preserving positivity, accuracy, and computational time efficiency. Numerical results illustrate the interest of the approach., This work has been partially supported by the European Union in the FP7- PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Econom´ıa y Competitividad Spanish Grant MTM2013-41765-P.