A Semigroup Expansion for Pricing Barrier Options. (14th September 2014)

• Record Type: Journal Article
• Authors: Kato, Takashi; Takahashi, Akihiko; Yamada, Toshihiro
• Other Names: Stettner Lukasz Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2014(2014)
• Publication Date: 2014-09-14
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2014/268086
• Languages: English
• ISSNs: 2090-3332

Abstract

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.