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Pricing Discrete Barrier Options Under Stochastic Volatility

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Abstract

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with discrete monitoring. To the best of our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Furthermore, it provides numerical examples for pricing double barrier call options with discrete monitoring under Heston and λ-SABR models.

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Authors and Affiliations

  1. Graduate School of Economics, The University of Tokyo, Tokyo, Japan

    Kenichiro Shiraya & Akihiko Takahashi

  2. Mizuho-DL Financial Technology Co., Ltd., Tokyo, Japan

    Kenichiro Shiraya

  3. Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. (MTEC), Tokyo, Japan

    Toshihiro Yamada

Authors
  1. Kenichiro Shiraya
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  2. Akihiko Takahashi
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  3. Toshihiro Yamada
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Corresponding author

Correspondence to Toshihiro Yamada.

Additional information

This research is supported by CARF (Center for Advanced Research in Finance), Graduate School of Economics, the University of Tokyo.

All the contents expressed in this research are solely those of the authors and do not represent the view of Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd.(MTEC), Mizuho-DL Financial Technology Co., Ltd. or any other institutions. The authors are not responsible or liable in any manner for any losses and/or damages caused by the use of any contents in this research.

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Shiraya, K., Takahashi, A. & Yamada, T. Pricing Discrete Barrier Options Under Stochastic Volatility. Asia-Pac Financ Markets 19, 205–232 (2012). https://doi.org/10.1007/s10690-011-9147-3

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  • DOI: https://doi.org/10.1007/s10690-011-9147-3

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