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New Acceleration Schemes with the Asymptotic Expansion in Monte Carlo Simulation (Revised in June 2005, subsequently published in "Advances in Mathematical Economics", Vol.8, 411-431, 2006. )

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  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Yoshihiko Uchida

    (Institute for Monetary and Economic Studies, Bank of Japan)

Abstract

In the present paper, we propose a new computational technique with the Asymptotic Expansion (AE) approach to achieve variance reduction of the Monte-Carlo integration appearing especially in finance. We extend the algorithm developed by Takahashi and Yoshida (2003) to the second order asymptotics. Moreover, we apply the AE to approximate time dependent differentials of the target value in Newton (1994)'s scheme. Our numerical examples include pricing of average and basket options when the underlying state variables follow Constant Elasticity of Variance (CEV) processes.

Suggested Citation

  • Akihiko Takahashi & Yoshihiko Uchida, 2004. "New Acceleration Schemes with the Asymptotic Expansion in Monte Carlo Simulation (Revised in June 2005, subsequently published in "Advances in Mathematical Economics", Vol.8, 411-431, 2006. ," CARF F-Series CARF-F-012, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf012
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    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/9.pdf
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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. 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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