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A Semi-group Expansion for Pricing Barrier Options

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  • Takashi Kato
  • Akihiko Takahashi
  • Toshihiro Yamada

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.

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  • Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2012. "A Semi-group Expansion for Pricing Barrier Options," Papers 1202.3002, arXiv.org, revised Jun 2013.
    • Handle: RePEc:arx:papers:1202.3002
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    File URL: http://arxiv.org/pdf/1202.3002
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    References listed on IDEAS

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    1. Kenichiro Shiraya & Akihiko Takahashi & Toshihiro Yamada, 2010. "Pricing Discrete Barrier Options under Stochastic Volatility," CARF F-Series CARF-F-210, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2011.
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