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A Remark on a Singular Perturbation Method for Option Pricing under a Stochastic Volatility

Author

Listed:
  • Kyo Yamamoto

    (Graduate School of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

This paper studies the accuracy of a singular perturbation method for option pricing under a stochastic volatility model ([8]). First, through numerical experiments we confirm that the first order approximation provides sufficiently accurate option prices in a fast mean-reversion case of the volatility process while it does not in a non-fast mean-reversion case. Then, we derive the second order approximation formula and examine the improvement of the approximation.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2008cf597
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    Citations

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    Cited by:

    1. 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.
    2. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CIRJE F-Series CIRJE-F-874, CIRJE, Faculty of Economics, University of Tokyo.
    3. Kyo Yamamoto & Seisho Sato & Akihiko Takahashi, 2008. "Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment ( Revised in May 2009; Electronic version of an article will be published in "International Journal," CARF F-Series CARF-F-138, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Akihiko Takahashi & Masashi Toda, 2012. "Note on an Extension of an Asymptotic Expansion Scheme," CARF F-Series CARF-F-286, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2012.
    5. Kyo Yamamoto & Seisho Sato & Akihiko Takahashi, 2009. "Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-625, CIRJE, Faculty of Economics, University of Tokyo.
    6. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-305, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. 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.
    8. 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.

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