Advanced Search
MyIDEAS: Login to save this article or follow this journal

Modeling fat tails in stock returns: a multivariate stable-GARCH approach

Contents:

Author Info

  • Matteo Bonato

    ()

Registered author(s):

    Abstract

    In this paper a new multivariate volatility model is proposed. It combines the appealing properties of the stable Paretian distribution to model the heavy tails with the GARCH model to capture the volatility clustering. Returns on assets are assumed to follow a sub-Gaussian distribution, which is a particular multivariate stable distribution. In this way the characteristic function of the fitted returns has a tractable expression and the density function can be recovered by numerical methods. A multivariate GARCH structure is then adopted to model the covariance matrix of the Gaussian vectors underlying the sub-Gaussian system. The model is applied to a bivariate series of daily U.S. stock returns. Value-at-risk for long and short positions is computed and compared with the one obtained using the multivariate normal and the multivariate Student’s t distribution. Finally, exploiting the recent developments in the vast dimensional time-varying covariances modeling, possible feasible extensions of our model to higher dimensions are suggested and an illustrative example using the Dow Jones index components is presented. Copyright Springer-Verlag 2012

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://hdl.handle.net/10.1007/s00180-011-0270-4
    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 under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Springer in its journal Computational Statistics.

    Volume (Year): 27 (2012)
    Issue (Month): 3 (September)
    Pages: 499-521

    as in new window
    Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:499-521

    Contact details of provider:
    Web page: http://www.springerlink.com/link.asp?id=120306

    Order Information:
    Web: http://link.springer.de/orders.htm

    Related research

    Keywords: Stable Paretian distributions; Fourier transform; Value-at-risk; High dimensional modeling; C13; C51; G17;

    Find related papers by JEL classification:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Neil Shephard & Kevin Sheppard & Robert F. Engle, 2008. "Fitting vast dimensional time-varying covariance models," Economics Series Working Papers 403, University of Oxford, Department of Economics.
    2. J. Huston McCulloch, 2003. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty," Working Papers 03-07, Ohio State University, Department of Economics.
    3. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
    4. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    5. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    6. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    8. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    9. Toker Doganoglu & Christoph Hartz & Stefan Mittnik, 2007. "Portfolio optimization when risk factors are conditionally varying and heavy tailed," Computational Economics, Society for Computational Economics, vol. 29(3), pages 333-354, May.
    10. LOMBARDI, Marco & VEREDAS, David, 2007. "Indirect estimation of elliptical stable distributions," CORE Discussion Papers 2007018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 639-61, October.
    12. Ruiz, Esther & Pascual, Lorenzo, 2002. " Bootstrapping Financial Time Series," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 271-300, July.
    13. GARCIA, René & RENAULT, Eric & VEREDAS, David, 2006. "Estimation of stable distributions by indirect inference," CORE Discussion Papers 2006112, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Bonato, Matteo, 2011. "Robust estimation of skewness and kurtosis in distributions with infinite higher moments," Finance Research Letters, Elsevier, vol. 8(2), pages 77-87, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:27:y:2012:i:3:p:499-521. 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: (Guenther Eichhorn) or (Christopher F Baum).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.