An FBSDE Approach to American Option Pricing with an Interacting Particle Method
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.
Year of publication: |
2012-11
|
---|---|
Authors: | Fujii, Masaaki ; Sato, Seisho ; Takahashi, Akihiko |
Institutions: | arXiv.org |
Saved in:
freely available
Saved in favorites
Similar items by person
-
Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility
Fujii, Masaaki, (2012)
-
Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows
Fujii, Masaaki, (2014)
-
Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method
Fujii, Masaaki, (2012)
- More ...