We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results.

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Series arXiv.org e-Print archive
Bouchard, B, Chau, K.W, Manai, A, & Sid-Ali, A. (2017). Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view. arXiv.org e-Print archive.