In the paper, we propose a new calculation scheme for American options
in the framework of a forward backward stochastic di erential 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 & Takahashi (2012c), 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 e ectiveness of the particle method.