IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v63y2003i3p275-286.html
   My bibliography  Save this article

Elliptical copulas: applicability and limitations

Author

Listed:
  • Frahm, Gabriel
  • Junker, Markus
  • Szimayer, Alexander

Abstract

We study copulas generated by elliptical distributions. We show that their tail dependence can be simply computed with default routines on Student's t-distribution given Kendall's [tau] and the tail index. The copula family generated by the sub-Gaussian [alpha]-stable distribution is unable to cover the size of tail dependence observed in financial data.

Suggested Citation

  • Frahm, Gabriel & Junker, Markus & Szimayer, Alexander, 2003. "Elliptical copulas: applicability and limitations," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 275-286, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:3:p:275-286
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00092-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. Sergio Ortobelli & Isabella Huber & Eduardo Schwartz, 2002. "Portfolio selection with stable distributed returns," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 265-300, May.
    2. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    3. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    4. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    5. 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.
    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. Bao, Te & Diks, Cees & Li, Hao, 2018. "A generalized CAPM model with asymmetric power distributed errors with an application to portfolio construction," Economic Modelling, Elsevier, vol. 68(C), pages 611-621.
    2. Langworthy, Benjamin W. & Stephens, Rebecca L. & Gilmore, John H. & Fine, Jason P., 2021. "Canonical correlation analysis for elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Gungor, Sermin & Luger, Richard, 2009. "Exact distribution-free tests of mean-variance efficiency," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 816-829, December.
    4. Mendes, Beatriz Vaz de Melo & Arslan, Olcay, 2006. "Multivariate Skew Distributions Based on the GT-Copula," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(2), November.
    5. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    6. Adcock, C J & Meade, N, 2017. "Using parametric classification trees for model selection with applications to financial risk management," European Journal of Operational Research, Elsevier, vol. 259(2), pages 746-765.
    7. Sermin Gungor & Richard Luger, 2016. "Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 161-175, April.
    8. Hassan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi, 2016. "Elliptical tempered stable distribution," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1069-1087, July.
    9. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013, January-A.
    10. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    11. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    12. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    13. GUORUI BIAN & MICHAEL McALEER & WING-KEUNG WONG, 2013. "Robust Estimation And Forecasting Of The Capital Asset Pricing Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 1-18.
    14. Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
    15. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    16. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    17. 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.
    18. 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.
    19. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2016. "Copula--based Specification of vector MEMs," Papers 1604.01338, arXiv.org.
    20. Gijbels, Irène & Kika, Vojtěch & Omelka, Marek, 2021. "On the specification of multivariate association measures and their behaviour with increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 182(C).

    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:eee:stapro:v:63:y:2003:i:3:p:275-286. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.