CIRJE-F-871 "An FBSDE Approach to American Option Pricing with an Interacting Particle Method"
Author Name

Fujii, Masaaki, Seisho Sato and Akihiko Takahashi

Date November 2012
Full Paper   PDF file
Remarks Revised version of CIRJE-F-621 (2009); a part of this paper was published in International Journal of Theoretical and Applied Finance Vol.15-6, 2012 as ``A General Computation Scheme for a High-Order Asymptotic Expansion Method" (as CIRJE-F-787).  

Revised in October 2014; Forthcoming in Asia-Pacific Financial Markets.
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 exising tree algorithms shows the effectiveness of the particle method.