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A Semi-group Expansion for Pricing Barrier Options

Takashi Kato, 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)

No CIRJE-F-841, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Date: 2012-02
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