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A Weak Approximation with Asymptotic Expansion and Multidimensional Malliavin Weights

Author

Listed:
  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

  • Toshihiro Yamada

    (Graduate School of Economics, The University of Tokyo & MTEC)

Abstract

　　 This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic expansion to compute a target expectation value precisely. The mathematical validity is given based on Watanabe and Kusuoka theories in Malliavin calculus. Moreover, numerical experiments for option pricing under local and stochastic volatility models confirm the effectiveness of our scheme.

Suggested Citation

  • Akihiko Takahashi & Toshihiro Yamada, 2013. "A Weak Approximation with Asymptotic Expansion and Multidimensional Malliavin Weights," CIRJE F-Series CIRJE-F-909, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2013cf909
    as

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2013/2013cf909.pdf
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    References listed on IDEAS

    as
    1. Hideyuki Tanaka & Toshihiro Yamada, 2013. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method (Forthcoming in "International Journal of Theoretical and Applied Finance")," CARF F-Series CARF-F-333, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. 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.
    3. Hideyuki Tanaka & Toshihiro Yamada, 2012. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method," Papers 1210.0670, arXiv.org, revised Nov 2013.
    4. Akihiko Takahashi & Masashi Toda, 2013. "Note On An Extension Of An Asymptotic Expansion Scheme," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-23.
    5. Masaaki Fujii, 2012. "Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering," Papers 1209.1893, arXiv.org, revised Mar 2013.
    6. Masaaki Fujii, 2013. "Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering," CIRJE F-Series CIRJE-F-883, CIRJE, Faculty of Economics, University of Tokyo.
    7. 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.
    8. Akihiko Takahashi & Masashi Toda, 2013. "Note on an Extension of an Asymptotic Expansion Scheme," CARF F-Series CARF-F-312, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Masaaki Fujii, 2012. "Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering," CARF F-Series CARF-F-311, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Mar 2013.
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