CIRJE-F-841 "A Semi-group Expansion for Pricing Barrier Options"
Author Name Kato, Takashi, Akihiko Takahashi and Toshihiro Yamada
Date February 2012
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Remarks Revised in March 2012, April 2012, June 2013 and August 2014. Forthcoming in International Journal of Stochastic Analysis.
  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.