A Semi-group Expansion for Pricing Barrier Options
Akihiko Takahashi and
Toshihiro Yamada Additional contact information Takashi Kato: Graduate School of Engineering Science, Osaka University
Akihiko Takahashi: Faculty of Economics, University of Tokyo
Toshihiro Yamada: Mitsubishi UFJ T rust Investment Technology Institute Co.,Ltd. (MTEC)
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.