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Pricing Discrete Barrier Options under Stochastic Volatility

Author

Listed:
  • Kenichiro Shiraya

    (Mizuho-DL Financial Technology Co., Ltd.)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Toshihiro Yamada

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

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 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 ă-SABR models.

Suggested Citation

  • 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.
    • Handle: RePEc:cfi:fseres:cf210
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    References listed on IDEAS

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    1. 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.
    2. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    3. Maria Siopacha & Josef Teichmann, 2007. "Weak and Strong Taylor methods for numerical solutions of stochastic differential equations," Papers 0704.0745, arXiv.org.
    4. 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.
    5. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-682, CIRJE, Faculty of Economics, University of Tokyo.
    6. 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.
    7. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Average Options under Stochastic Volatility Models," CARF J-Series CARF-J-059, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Akihiko Takahashi & Toshihiro Yamada, 2009. "An Asymptotic Expansion with Push-Down of Malliavin Weights," CIRJE F-Series CIRJE-F-695, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

    1. Kenichiro Shiraya, 2016. "An approximation method for pricing continuous barrier options under multi-asset local stochastic volatility models (Forthcoming in International Journal of Theoretical and Applied Finance.)," CARF F-Series CARF-F-397, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2018.
    2. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2012. "A Semi-group Expansion for Pricing Barrier Options," CIRJE F-Series CIRJE-F-841, CIRJE, Faculty of Economics, University of Tokyo.
    3. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2012. "A Semi-group Expansion for Pricing Barrier Options," Papers 1202.3002, arXiv.org, revised Jun 2013.
    4. Colin Turfus & Alexander Shubert, 2017. "ANALYTIC PRICING OF CoCo BONDS," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-26, August.
    5. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2012. "Semi-group Expansion for Pricing Barrier Options," CARF F-Series CARF-F-271, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2013.
    6. Akihiko Takahashi & Toshihiro Yamada, 2014. "On Error Estimates for Asymptotic Expansions with Malliavin Weights -Application to Stochastic Volatility Model- (Revised version of CARF-F-324; Forthcoming in "Mathematics of Operations Research," CARF F-Series CARF-F-347, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2014.
    7. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382, arXiv.org.

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