IDEAS home Printed from https://ideas.repec.org/p/usi/wpaper/702.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://repec.deps.unisi.it/quaderni/702.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    3. Hatem Ben‐Ameur & Rim Chérif & Bruno Rémillard, 2020. "Dynamic programming for valuing American options under a variance‐gamma process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(10), pages 1548-1561, October.
    4. Claudia Yeap & Simon S Kwok & S T Boris Choy, 2018. "A Flexible Generalized Hyperbolic Option Pricing Model and Its Special Cases," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 425-460.
    5. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    6. Kaehler, Jürgen, 1991. "Modelling and forecasting exchange-rate volatility with ARCH-type models," ZEW Discussion Papers 91-02, ZEW - Leibniz Centre for European Economic Research.
    7. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    8. Abootaleb Shirvani & Yuan Hu & Svetlozar T. Rachev & Frank J. Fabozzi, 2019. "Option Pricing with Mixed Levy Subordinated Price Process and Implied Probability Weighting Function," Papers 1910.05902, arXiv.org, revised Apr 2020.
    9. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    10. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    11. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    12. Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche 9615, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers 2008-13, Department of Economics and Business Economics, Aarhus University.
    14. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    15. Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
    16. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    17. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    19. René Garcia & Richard Luger & Éric Renault, 2005. "Viewpoint: Option prices, preferences, and state variables," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(1), pages 1-27, February.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:usi:wpaper:702. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Fabrizio Becatti (email available below). General contact details of provider: https://edirc.repec.org/data/desieit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.