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

Masaaki Fujii, Seisho Sato () and Akihiko Takahashi

Asia-Pacific Financial Markets, 2015, vol. 22, issue 3, 239-260

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 ( 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. Copyright Springer Japan 2015

Keywords: BSDE; FBSDE; Asymptotic expansion; Perturbation; Particle method; 65C30 (search for similar items in EconPapers)
Date: 2015
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Handle: RePEc:kap:apfinm:v:22:y:2015:i:3:p:239-260