An FBSDE Approach to American Option Pricing with an Interacting Particle Method
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 (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 third-order analysis for the Heston model. The comparison to those obtained from existing tree algorithms shows the effectiveness of the particle method.
Keywords
Cite
@article{arxiv.1211.5867,
title = {An FBSDE Approach to American Option Pricing with an Interacting Particle Method},
author = {Masaaki Fujii and Seisho Sato and Akihiko Takahashi},
journal= {arXiv preprint arXiv:1211.5867},
year = {2012}
}
Comments
18 pages, 5 tables