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A note on the Estimation of a Gamma-Variance Process: Learning from a Failure

Author

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  • Gian P. Cervellera

    (Università di Siena)

  • Marco P. Tucci

    (Università di Siena)

Abstract

This paper confirms that, as originally reported in Seneta (Journal of Applied Probability 41:177–187, 2004, p. 183), it is impossible to replicate Madan et al. (European Finance Review 2:135–156, 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 finding maximum likelihood estimates of the parameters of the popular VG model. Both standard econometric software, such as R, low level programming languages, such as Matlab $$^{\textregistered }$$ ® , and non-standard optimization software, such as Ezgrad described in Tucci (Journal of Economic Dynamics and Control 26:1739–1764, 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. An intuitive procedure which works nicely both when implemented in R and in Matlab $$^{\textregistered }$$ ® is presented.

Suggested Citation

  • Gian P. Cervellera & Marco P. Tucci, 2017. "A note on the Estimation of a Gamma-Variance Process: Learning from a Failure," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 363-385, March.
    • Handle: RePEc:kap:compec:v:49:y:2017:i:3:d:10.1007_s10614-016-9566-3
    DOI: 10.1007/s10614-016-9566-3
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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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