An FBSDE Approach to American Option Pricing with an Interacting Particle Method

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into the form of a decoupled non-linear FBSDE. We numerically solve the FBSDE by applying an interacting particle method recently proposed by Fujii and Takahashi (2012d), which allows one to perform a Monte Carlo simulation in a fully forward-looking manner. We perform the fourth-order analysis for the Black-Scholes (BS) model and the third-order analysis for the Heston model. The comparison to those obtained from existing tree algorithms shows the effectiveness of the particle method.