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Pricing Barrier and Average Options under Stochastic Volatility Environment

Author

Listed:
  • Kenichiro Shiraya

    (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 lambda-SABR and SABR models.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CARF F-Series CARF-F-176, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised May 2010.
    • Handle: RePEc:cfi:fseres:cf176
    as

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    References listed on IDEAS

    as
    1. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method (Published in "Journal of Japan Statistical Society", Vol.35-2, 171-203, 2005. )," CARF F-Series CARF-F-030, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Kyo Yamamoto & Akihiko Takahashi, 2008. "A Remark on a Singular Perturbation Method for Option Pricing under a Stochastic Volatility," CIRJE F-Series CIRJE-F-597, CIRJE, Faculty of Economics, University of Tokyo.
    3. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    4. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    5. 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.
    6. 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.
    7. Kyo Yamamoto & Akihiko Takahashi, 2008. "A Remark on a Singular Perturbation Method for Option Pricing under a Stochastic Volatility Model ( Forthcoming in "Asia-Pacific Financial Markets". )," CARF F-Series CARF-F-139, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    9. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    10. 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.
    11. 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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