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

18 Pages Posted: 26 Nov 2012

See all articles by Masaaki Fujii

Masaaki Fujii

University of Tokyo - Faculty of Economics

Seisho Sato

Graduate School of Economics, The University of Tokyo

Akihiko Takahashi

University of Tokyo - Faculty of Economics

Date Written: November 26, 2012

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 & 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.

Keywords: BSDE, FBSDE, asymptotic expansion, perturbation, particle method

JEL Classification: G13, C15

Suggested Citation

Fujii, Masaaki and Sato, Seisho and Takahashi, Akihiko, An FBSDE Approach to American Option Pricing with an Interacting Particle Method (November 26, 2012). Available at SSRN: https://ssrn.com/abstract=2180696 or http://dx.doi.org/10.2139/ssrn.2180696

Masaaki Fujii (Contact Author)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Seisho Sato

Graduate School of Economics, The University of Tokyo ( email )

Hongo 7-3-1
Bunkyo-ku
Tokyo 113-0033
Japan

Akihiko Takahashi

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
113
Abstract Views
1,110
Rank
438,854
PlumX Metrics