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

• Main Authors: Bouchard Bruno, Wai Chau Ki, Manai Arij, Sid-Ali Ahmed
• Format: Article
• Language: English
• Published: EDP Sciences 2019-01-01
• Series: ESAIM: Proceedings and Surveys
• Subjects: american options; viscosity solution; semilinear black and scholes partial differential equation; branching method; bsde
• Online Access: https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196512.pdf

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.