An Asymptotic Expansion for Solutions of Cauchy-Dirichlet Problem for Second Order Parabolic PDEs and its Application to Pricing Barrier Options

Takashi Kato, Akihiko Takahashi and Toshihiro Yamada
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Takashi Kato: Graduate School of Mathematical Sciences, University of Tokyo
Akihiko Takahashi: Faculty of Economics, University of Tokyo
Toshihiro Yamada: Mitsubishi UFJ Trust Investment Technology Institute Co.,Ltd. (MTEC)

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

Abstract: This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing a barrier option under a certain type of stochastic volatility model including the log-normal SABR model.

Date: 2012-02
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