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

TL;DR

This paper extends the mathematical framework for American option pricing to multi-dimensional cases using semilinear PDEs and introduces two new numerical schemes, demonstrating the effectiveness of randomization over polynomial approximation.

Contribution

It generalizes viscosity solution characterization for American options to multi-dimensional payoffs and proposes two novel numerical schemes based on branching processes.

Findings

Randomization procedure yields accurate results

Polynomial approximation of the driver is inefficient

New schemes outperform existing methods in experiments

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 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.