A Semi-group Expansion for Pricing Barrier Options
  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. 
Takashi Kato, Akihiko Takahashi and Toshihiro Yamada
q-fin.CP math.AP math.PR