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

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.