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Pricing Barrier and Average Options under Stochastic Volatility Environment

Author

Listed:
  • Kenichiro Shiraya

    (Graduate School of Economics, University of Tokyo, Mizuho-DL Financial Technology Co., Ltd.)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Masashi Toda

    (Graduate School of Economics, University of Tokyo)

Abstract

This paper proposes a new approximation method of pricing barrier and average options under stochastic volatility environment by applying an asymptotic expansion approach. In particular, a high-order expansion scheme for general multi-dimensional diffusion processes is effectively applied. Moreover, the paper combines a static hedging method with the asymptotic expansion method for pricing barrier options. Finally, numerical examples show that the fourth or fifth-order asymptotic expansion scheme provides sufficiently accurate approximations under the ă-SABR and SABR models.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2010. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-745, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2010cf745
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2010/2010cf745.pdf
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    References listed on IDEAS

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    1. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    2. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
    3. Yoshifumi Muroi, 2005. "Pricing contingent claims with credit risk: Asymptotic expansion approach," Finance and Stochastics, Springer, vol. 9(3), pages 415-427, July.
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