Asia-Pacific Financial Markets

, Volume 22, Issue 3, pp 239–260 | Cite as

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

  • Masaaki Fujii
  • Seisho Sato
  • Akihiko Takahashi


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 (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 effectiveness of the particle method.


BSDE FBSDE Asymptotic expansion Perturbation  Particle method 

Mathematics Subject Classification



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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Graduate School of EconomicsUniversity of TokyoBunkyo-kuJapan

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