IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v13y2006i1p19-38.html
   My bibliography  Save this article

On the Distributional Characterization of Daily Log-Returns of a World Stock Index

Author

Listed:
  • Kevin Fergusson
  • Eckhard Platen

Abstract

In this paper distributions are identified which suitably fit log-returns of the world stock index when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized hyperbolic distributions the maximum likelihood estimates appear to cluster in the neighbourhood of those of the Student t distribution. This is confirmed at a high significance level under the likelihood ratio test. Finally, the paper derives the minimal market model, which explains the empirical findings as a consequence of the optimal market dynamics.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:19-38
    DOI: 10.1080/13504860500394052
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500394052
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters,in: Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335 World Scientific Publishing Co. Pte. Ltd..
    3. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    4. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Computational Statistics, Springer, vol. 18(3), pages 355-373, September.
    5. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of Inference," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 207-219, November.
    7. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    9. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    10. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    11. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 221-247, November.
    13. 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.
    14. 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.
    15. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    16. repec:wsi:ijtafx:v:07:y:2004:i:04:n:s0219024904002499 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    World stock index; log-return distribution; Student t distribution; symmetric generalized hyperbolic distribution;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:taf:apmtfi:v:13:y:2006:i:1:p:19-38. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.