An Asymptotic Expansion for Solutions of Cauchy-Dirichlet Problem for Second Order ParabolicPDEs and its Application to Pricing Barrier Options(Revised as CARF-F-349, in August 2014)

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.