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A New Improvement Scheme for Approximation Methods of Probability Density Functions

Listed author(s):
  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Yukihiro Tsuzuki

    (Graduate School of Economics, University of Tokyo)

Registered author(s):

    This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in best approximation in an inner product space . Moreover, we applies "Dykstra's cyclic projections algorithm" for its implementation. Numerical examples for application to an asymptotic expansion method in option pricing demonstrate the effectiveness of our scheme under Black-Scholes and SABR models.

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    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-874.

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    Length: 23 pages
    Date of creation: Jan 2013
    Handle: RePEc:tky:fseres:2013cf874
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    1. Akihiko Takahashi & Kohta Takehara, 2010. "A Hybrid Asymptotic Expansion Scheme: An Application To Long-Term Currency Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1179-1221.
    2. Kyo Yamamoto & Seisho Sato & Akihiko Takahashi, 2008. "Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-596, CIRJE, Faculty of Economics, University of Tokyo.
    3. Akihiko Takahashi & Kohta Takehara, 2010. "A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options," CIRJE F-Series CIRJE-F-734, CIRJE, Faculty of Economics, University of Tokyo.
    4. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480.
    5. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
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