Asia-Pacific Financial Markets

, Volume 11, Issue 4, pp 393–430 | Cite as

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

  • Ryosuke Matsuoka
  • Akihiko Takahashi
  • Yoshihiko Uchida


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.


asymptotic expansion approach option pricing Greeks CEV process Monte Carlo simulation variance reduction method 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Ryosuke Matsuoka
    • 1
  • Akihiko Takahashi
    • 2
  • Yoshihiko Uchida
    • 3
  1. 1.1Herrill Lynch Japan Securities Co., Ltd.TokyoUSA
  2. 2.Graduate School of EconomicsThe University of TokyoTokyoUSA
  3. 3.Graduate School of EconomicsOsaka UniversityosakaUSA

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