A Semigroup Expansion for Pricing Barrier Options. (14th September 2014) - Kato, Takashi; Takahashi, Akihiko; Yamada, Toshihiro
Abstract : This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develop a semigroup 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.