Table of Contents
International Journal of Stochastic Analysis
Volume 2014, Article ID 268086, 15 pages
http://dx.doi.org/10.1155/2014/268086
Research Article

A Semigroup Expansion for Pricing Barrier Options

1Division of Mathematical Science for Social Systems, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan
2Graduate School of Economics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
3Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. (MTEC), 2-6, Akasaka 4-Chome, Minato, Tokyo 107-0052, Japan

Received 20 April 2014; Accepted 11 August 2014; Published 14 September 2014

Academic Editor: Lukasz Stettner

Copyright © 2014 Takashi Kato et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develop a semigroup expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, we propose a concrete approximation formula under a stochastic volatility model and demonstrate its validity by some numerical experiments.