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

TL;DR

This paper introduces a novel FBSDE-based numerical scheme for American option pricing using an interacting particle method, demonstrating improved accuracy over traditional tree algorithms in Black-Scholes and Heston models.

Contribution

It develops a new FBSDE approach combined with an interacting particle method for American option valuation, offering a fully forward-looking Monte Carlo simulation technique.

Findings

Effective in Black-Scholes model with fourth-order accuracy

Accurate in Heston model with third-order analysis

Outperforms existing tree algorithms in numerical tests

Abstract

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.