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Pricing Discrete Barrier Options Under Stochastic Volatility

Author

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  • Kenichiro Shiraya
  • Akihiko Takahashi
  • Toshihiro Yamada

    ()

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. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi & Toshihiro Yamada, 2012. "Pricing Discrete Barrier Options Under Stochastic Volatility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(3), pages 205-232, September.
  • Handle: RePEc:kap:apfinm:v:19:y:2012:i:3:p:205-232 DOI: 10.1007/s10690-011-9147-3
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    References listed on IDEAS

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    1. Gianluca Fusai & I. Abrahams & Carlo Sgarra, 2006. "An exact analytical solution for discrete barrier options," Finance and Stochastics, Springer, vol. 10(1), pages 1-26, January.
    2. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    3. Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
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    Citations

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    Cited by:

    1. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2014. "A Semi-group Expansion for Pricing Barrier Options," CARF F-Series CARF-F-349, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Kenichiro Shiraya, 2016. "An approximation method for pricing continuous barrier options under multi-asset local stochastic volatility models," CARF F-Series CARF-F-397, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Shiraya, Kenichiro & Takahashi, Akihiko, 2017. "A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance," European Journal of Operational Research, Elsevier, vol. 258(1), pages 358-371.
    4. Akihiko Takahashi & Toshihiro Yamada, 2016. "An Asymptotic Expansion for Forward–Backward SDEs: A Malliavin Calculus Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, pages 337-373.
    5. Akihiko Takahashi & Toshihiro Yamada, 2014. "This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More gene," CARF F-Series CARF-F-347, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2014.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2017. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models (Revised version of CARF-F-365 : Forthcoming in Mathematics of Operations Research)," CARF F-Series CARF-F-426, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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