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

Masaaki Fujii, Seisho Sato and Akihiko Takahashi
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Masaaki Fujii: The University of Tokyo
Seisho Sato: The Institute of Statistical Mathematics
Akihiko Takahashi: The University of Tokyo

No CARF-F-302, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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 wellknown 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 (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 thirdorder analysis for the Heston model. The comparison to those obtained from existing tree algorithms shows the effectiveness of the particle method.

Pages: 19 pages
Date: 2012-11
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Citations: View citations in EconPapers (11)

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