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A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach (Special Issue on Mathematical Finance, Published in "Asia-Pacific Financial Markets", Vol.11, 393-430, 2006. )

Author

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  • Matsuoka Ryosuke

    (Tokyo Marine & Nichido Fire Insurance co., Ltd.)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Yoshihiko Uchida

    (Graduate School of Economics, Osaka University)

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 European call options under general Markovian processes of underlying asset 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.

Suggested Citation

  • Matsuoka Ryosuke & Akihiko Takahashi & Yoshihiko Uchida, 2005. "A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach (Special Issue on Mathematical Finance, Published in "Asia-Pacific Financial Markets", Vol.11, 393-430, 2," CARF F-Series CARF-F-044, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  • Handle: RePEc:cfi:fseres:cf044
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    File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/45.pdf
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