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A note on the estimation of a Gamma-Variance process: Learning from a failure

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  • Gian P. Cervellera
  • Marco P. Tucci

Abstract

This paper con?rms that, as originally reported in Seneta (2004, p. 183), it is impossible to replicate Madan et al.?s (1998) results using log daily returns on S&P 500 Index from January 1992 to September 1994. This failure leads to a close investigation of the computational problems associated with ?nding maximum likelihood estimates of the parameters of the popular VG model. Both standard econometric software, such as R, and non-standard optimization software, such as Ezgrad described in Tucci (2002), are used. The complexity of the log-likelihood function is studied. It is shown that it looks very complicated, with many local optima, and may be incredibly sensitive to very small changes in the sample used. Adding or removing a single observation may cause huge changes both in the maximum of the log-likelihood function and in the estimated parameter values.

Suggested Citation

  • Gian P. Cervellera & Marco P. Tucci, 2014. "A note on the estimation of a Gamma-Variance process: Learning from a failure," Department of Economics University of Siena 702, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:702
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    File URL: http://repec.deps.unisi.it/quaderni/702.pdf
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    References listed on IDEAS

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    1. Farzad Fard & Ning Rong, 2014. "Pricing and managing risks of ruin contingent life annuities under regime switching variance gamma process," Annals of Finance, Springer, vol. 10(2), pages 315-332, May.
    2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    3. Elton A. Daal & Dilip B. Madan, 2005. "An Empirical Examination of the Variance-Gamma Model for Foreign Currency Options," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2121-2152, November.
    4. Ariel Almendral & Cornelis W. Oosterlee, 2007. "On American Options Under the Variance Gamma Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 131-152.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Variance-Gamma; log stock returns; maximum likelihood estimation; globally optimizing procedures;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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