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New Acceleration Schemes with the Asymptotic Expansion in Monte Carlo Simulation

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Author Info

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Yoshihiko Uchida

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

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    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, basket and swap options when the underlying state variables follow Constant Elasticity of Variance (CEV) processes.

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2004/2004cf298.pdf
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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-298.

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    Length: 31 pages
    Date of creation: Sep 2004
    Date of revision:
    Handle: RePEc:tky:fseres:2004cf298

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