IDEAS home Printed from https://ideas.repec.org/p/zbw/zewdip/9325.html
   My bibliography  Save this paper

On the modelling of speculative prices by stable Paretian distributions and regularly varying tails

Author

Listed:
  • Kaehler, Jürgen

Abstract

Earlier studies which applied the family of stable Paretian distributions to financial data are inconclusive and contradictory. In this article I estimate the parameters of the model by the Feuerverger-McDunnough method which enables the application of maximum likelihood rhethods. Based on inferential statistics, stable Paretian distributions can be rejected with monthly data. In order to confirm this result, the model is extended to the family of distributions with regularly varying tails. The result that stable Paretian distributions are not applicable is indeed confirmed by estimating the coefficient of regular variation.

Suggested Citation

  • Kaehler, Jürgen, 1993. "On the modelling of speculative prices by stable Paretian distributions and regularly varying tails," ZEW Discussion Papers 93-25, ZEW - Leibniz Centre for European Economic Research.
    • Handle: RePEc:zbw:zewdip:9325
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/29400/1/257108998.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Lau, Amy Hing-Ling & Lau, Hon-Shiang & Wingender, John R, 1990. "The Distribution of Stock Returns: New Evidence against the Stable Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 217-223, April.
    3. Hall, Joyce A. & Brorsen, B. Wade & Irwin, Scott H., 1989. "The Distribution of Futures Prices: A Test of the Stable Paretian and Mixture of Normals Hypotheses," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(1), pages 105-116, March.
    4. McFarland, James W & Pettit, R Richardson & Sung, Sam K, 1982. "The Distribution of Foreign Exchange Price Changes: Trading Day Effects and Risk Measurement," Journal of Finance, American Finance Association, vol. 37(3), pages 693-715, June.
    5. L. Wade, 1988. "Review," Public Choice, Springer, vol. 58(1), pages 99-100, July.
    6. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    7. Richard J Rogalski & Joseph D Vinso, 1978. "Empirical Properties of Foreign Exchange Rates," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 9(2), pages 69-79, June.
    8. Akgiray, Vedat & Booth, G Geoffrey, 1988. "Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 631-637, November.
    9. Jorge R Calderon-Rossell & Moshe Ben-Horim, 1982. "The Behavior of Foreign Exchange Rates," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 13(2), pages 99-111, June.
    10. Peter C.B. Phillips & Mico Loretan, 1990. "Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns," Cowles Foundation Discussion Papers 947, Cowles Foundation for Research in Economics, Yale University.
    11. Akgiray, Vedat & Booth, G Geoffrey, 1988. "The Stable-Law Model of Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 51-57, January.
    12. Michael L. Mussa, 1984. "The Theory of Exchange Rate Determination," NBER Chapters, in: Exchange Rate Theory and Practice, pages 13-78, National Bureau of Economic Research, Inc.
    13. Tucker, Alan L & Pond, Lallon, 1988. "The Probability Distribution of Foreign Exchange Price Changes: Tests of Candidate Processes," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 638-647, November.
    14. Akgiray, Vedat & Lamoureux, Christopher G, 1989. "Estimation of Stable-Law Parameters: A Comparative Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 85-93, January.
    15. Westerfield, Janice Moulton, 1977. "An examination of foreign exchange risk under fixed and floating rate regimes," Journal of International Economics, Elsevier, vol. 7(2), pages 181-200, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kaehler, Jürgen, 1993. "Forecasting volatility and option pricing for exchange-rate dynamics: a comparison of models," ZEW Discussion Papers 93-19, ZEW - Leibniz Centre for European Economic Research.

    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. Kaehler, Jürgen & Marnet, Volker, 1993. "Markov-switching models for exchange-rate dynamics and the pricing of foreign-currency options," ZEW Discussion Papers 93-03, ZEW - Leibniz Centre for European Economic Research.
    2. Lau, Hon-Shiang & Lau, Amy Hing Ling, 1997. "The confounding effects of distribution mixtures on some basic methods for handling stable-Paretian distributions," European Journal of Operational Research, Elsevier, vol. 100(1), pages 60-71, July.
    3. Tsionas, Efthymios G., 1998. "Monte Carlo inference in econometric models with symmetric stable disturbances," Journal of Econometrics, Elsevier, vol. 88(2), pages 365-401, November.
    4. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
    5. Canan G. Corlu & Alper Corlu, 2015. "Modelling exchange rate returns: which flexible distribution to use?," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1851-1864, November.
    6. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.
    7. Shengnan Li & Edward P. K. Tsang & John O'Hara, 2022. "Measuring relative volatility in high‐frequency data under the directional change approach," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 29(2), pages 86-102, April.
    8. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    9. Errunza, Vihang & Hogan, Kedreth Jr. & Mazumdar, Sumon C., 1996. "Behavior of international stock return distributions: A simple test of functional form," International Review of Economics & Finance, Elsevier, vol. 5(1), pages 51-61.
    10. Grobys, Klaus, 2023. "Correlation versus co-fractality: Evidence from foreign-exchange-rate variances," International Review of Financial Analysis, Elsevier, vol. 86(C).
    11. Lux, Thomas, 2006. "Financial power laws: Empirical evidence, models, and mechanism," Economics Working Papers 2006-12, Christian-Albrechts-University of Kiel, Department of Economics.
    12. Meade, Nigel, 2010. "Oil prices -- Brownian motion or mean reversion? A study using a one year ahead density forecast criterion," Energy Economics, Elsevier, vol. 32(6), pages 1485-1498, November.
    13. Pontines, Victor & Siregar, Reza, 2007. "The Yen, the US dollar, and the trade weighted basket of currencies: Does the choice of anchor currencies matter in identifying incidences of speculative attacks?," Japan and the World Economy, Elsevier, vol. 19(2), pages 214-235, March.
    14. Osler, Carol & Savaser, Tanseli, 2011. "Extreme returns: The case of currencies," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2868-2880, November.
    15. M. F. Omran, 1998. "An investigation of the maximal moments of exchange rates," Applied Economics Letters, Taylor & Francis Journals, vol. 5(10), pages 603-606.
    16. de Lima, Pedro J. F., 1997. "On the robustness of nonlinearity tests to moment condition failure," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 251-280.
    17. Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    18. Malz, Allan M., 1996. "Using option prices to estimate realignment probabilities in the European Monetary System: the case of sterling-mark," Journal of International Money and Finance, Elsevier, vol. 15(5), pages 717-748, October.
    19. van de Gucht, Linda M. & Dekimpe, Marnik G. & Kwok, Chuck C. Y., 1996. "Persistence in foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 15(2), pages 191-220, April.
    20. Cumperayot, Phornchanok & Kouwenberg, Roy, 2013. "Early warning systems for currency crises: A multivariate extreme value approach," Journal of International Money and Finance, Elsevier, vol. 36(C), pages 151-171.

    More about this item

    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:zbw:zewdip:9325. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/zemande.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.