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

Author

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  • 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)

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.

Suggested Citation

  • Ryosuke Matsuoka & Akihiko Takahashi & Yoshihiko Uchida, 2005. "A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach," CIRJE F-Series CIRJE-F-338, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2005cf338
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    1. Louis K. C. Chan & Hsiu-Lang Chen & Josef Lakonishok, 2002. "On Mutual Fund Investment Styles," Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1407-1437.
    2. Brown, Stephen J. & Goetzmann, William N., 1997. "Mutual fund styles," Journal of Financial Economics, Elsevier, vol. 43(3), pages 373-399, March.
    3. Fung, William & Hsieh, David A, 1997. "Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 275-302.
    4. Grinblatt, Mark & Titman, Sheridan & Wermers, Russ, 1995. "Momentum Investment Strategies, Portfolio Performance, and Herding: A Study of Mutual Fund Behavior," American Economic Review, American Economic Association, vol. 85(5), pages 1088-1105, December.
    5. Busse, Jeffrey A, 1999. "Volatility Timing in Mutual Funds: Evidence from Daily Returns," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1009-1041.
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