An FBSDE Approach to American Option Pricing with an Interacting Particle Method
18 Pages Posted: 26 Nov 2012
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: Suggested Citation
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