Quantitative Finance
F-series
Date:
Number:CARF-F-349
A Semi-group Expansion for Pricing Barrier Options (Revised version of CARF-F-271; 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.