Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

Abstract

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 reaction/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 discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results.

Keywords

• american options
• viscosity solution
• semilinear black and scholes partial differential equation
• branching method
• bsde