CIRJE-F-841 | "A Semi-group Expansion for Pricing Barrier Options" |
Author Name | Kato, Takashi, Akihiko Takahashi and Toshihiro Yamada |
Date | February 2012 |
Full Paper | PDF file |
Remarks | Revised in March 2012, April 2012, June 2013 and August 2014. Forthcoming in International Journal of Stochastic Analysis. |
Abstract |
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group 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. |