A Semi-Group Expansion for Pricing Barrier Options

Forthcoming in International Journal of Stochastic Analysis

29 Pages Posted: 18 Feb 2012 Last revised: 27 Aug 2014

See all articles by Takashi Kato

Takashi Kato

Association of Mathematical Finance Laboratory (AMFiL)

Akihiko Takahashi

University of Tokyo - Faculty of Economics

Toshihiro Yamada

Hitotsubashi University

Date Written: May 30, 2013

Abstract

This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing barrier option in the log-normal SABR stochastic volatility model.

Keywords: asymptotic expansion, The Cauchy-Dirichlet problem, second order parabolic PDEs, barrier options, stochastic volatility model

Suggested Citation

Kato, Takashi and Takahashi, Akihiko and Yamada, Toshihiro, A Semi-Group Expansion for Pricing Barrier Options (May 30, 2013). Forthcoming in International Journal of Stochastic Analysis, Available at SSRN: https://ssrn.com/abstract=2005663 or http://dx.doi.org/10.2139/ssrn.2005663

Takashi Kato

Association of Mathematical Finance Laboratory (AMFiL) ( email )

2-10
Kojimachi
Chiyoda, Tokyo 102-0083
Japan

Akihiko Takahashi

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Toshihiro Yamada (Contact Author)

Hitotsubashi University ( email )

2-1 Naka Kunitachi-shi
Tokyo 186-8601
Japan

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