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: Faculty of Economics, University of Tokyo
Seisho Sato: Faculty of Economics, University of Tokyo
Akihiko Takahashi: Faculty of Economics, University of Tokyo

No CIRJE-F-871, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: 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.

Pages: 21 pages
Date: 2012-11
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Citations: View citations in EconPapers (11)

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