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A New Improvement Scheme for Approximation Methods of Probability Density Functions

Author

Listed:
  • Akihiko Takahashi

    (The University of Tokyo)

  • Yukihiro Tsuzuki

    (The University of Tokyo)

Abstract

This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem. Moreover, we apply "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 SABR model.

Suggested Citation

  • Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-350, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf350
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    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F350.pdf
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    References listed on IDEAS

    as
    1. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    2. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2012. "A General Computation Scheme For A High-Order Asymptotic Expansion Method," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-25.
    3. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Options," CARF F-Series CARF-F-276, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Rama Cont, 2008. "Frontiers in Quantitative Finance: credit risk and volatility modeling," Post-Print hal-00437588, HAL.
    5. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2012. "A General Computation Scheme for a High-Order Asymptotic Expansion Method," CARF F-Series CARF-F-272, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Options," CARF F-Series CARF-F-290, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Optionss," CIRJE F-Series CIRJE-F-844, CIRJE, Faculty of Economics, University of Tokyo.
    8. Kenichiro Shiraya & Akihiko Takahashi, 2011. "Pricing average options on commodities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(5), pages 407-439, May.
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    Cited by:

    1. Sergio Albeverio & Francesco Cordoni & Luca Persio & Gregorio Pellegrini, 2019. "Asymptotic expansion for some local volatility models arising in finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 527-573, December.

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