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A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach

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Author Info

  • Ryosuke Matsuoka

    (Graduate School of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Yoshihiko Uchida

    (Graduate School of Economics, Osaka University)

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    Abstract

    We developed a new scheme for computing "Greeks"of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for deltas and vegas of plain vanilla and average call options under general Markovian processes of underlying asset prices. We also derived approximation formulae for gammas of plain vanilla and average call options, and for deltas of digital options under CEV(Constant Elasticity of Variance) processes of underlying assets' prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes confirmed the validity of our method.

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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-338.

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    Length: 34 pages
    Date of creation: Apr 2005
    Date of revision:
    Handle: RePEc:tky:fseres:2005cf338

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