|CIRJE-F-871||"An FBSDE Approach to American Option Pricing with an Interacting Particle Method"|
Fujii, Masaaki, Seisho Sato and Akihiko Takahashi
|Full Paper||PDF file|
|Remarks|| Revised version of CIRJE-F-621 (2009); a part of this paper was published in International Journal of Theoretical and Applied Finance Vol.15-6, 2012 as ``A General Computation Scheme for a High-Order Asymptotic Expansion Method" (as CIRJE-F-787). |
Revised in October 2014; Forthcoming in Asia-Pacific Financial Markets.
|In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic dierential 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.|