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


  • Matteo Bonato



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

Suggested Citation

  • Matteo Bonato, 2012. "Modeling fat tails in stock returns: a multivariate stable-GARCH approach," Computational Statistics, Springer, vol. 27(3), pages 499-521, September.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:499-521
    DOI: 10.1007/s00180-011-0270-4

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    References listed on IDEAS

    1. Ruiz, Esther & Pascual, Lorenzo, 2002. " Bootstrapping Financial Time Series," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 271-300, July.
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    3. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
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    10. Enrique Sentana, 1995. "Quadratic ARCH Models," Review of Economic Studies, Oxford University Press, vol. 62(4), pages 639-661.
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    Cited by:

    1. Meintanis, Simos G. & Ngatchou-Wandji, Joseph & Taufer, Emanuele, 2015. "Goodness-of-fit tests for multivariate stable distributions based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 171-192.
    2. Christian Francq & Simos G. Meintanis, 2016. "Fourier-type estimation of the power GARCH model with stable-Paretian innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(4), pages 389-424, May.

    More about this item


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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation


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