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

Bruno Bouchard (1) , Ki Wai Chau (2) , Arij Manai (3) , Ahmed Sid-Ali (4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CWI - Centrum voor Wiskunde en Informatica
3 UM - Le Mans Université
4 ULaval - Université Laval [Québec]

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.

Mots clés: American options; Viscosity solution; Semilinear Black and Sc- holes partial differential equation; Branching method; BSDE

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Bruno Bouchard, Ki Wai Chau, Arij Manai, Ahmed Sid-Ali. Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view. 2017. ⟨hal-01666399v1⟩