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Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution

  • Dongming Zhu
  • John Galbraith

Financial returns typically display heavy tails and some skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be especially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using a recent generalization of the asymmetric Student-t distribution to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial returns and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distribution is used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide empirical evidence for the usefulness of the generalized distribution in improving prediction of downside market risk of financial assets. De façon générale, les rendements financiers sont caractérisés par des queues épaisses et une certaine asymétrie. Ainsi, les modèles à variance conditionnelle dotés de ces caractéristiques donnent de meilleurs résultats que les modèles plus limités. La différence dans les résultats obtenus peut être particulièrement importante lorsqu'il s'agit d'évaluer des quantités qui dépendent des caractéristiques des queues, y compris les mesures du risque, tel que le manque à gagner prévu. Dans le cas actuel, en recourant à une généralisation récente de la distribution asymétrique suivant la loi t de Student, de sorte que des paramètres distincts limitent l'asymétrie et l'épaisseur de chaque queue, nous intégrons les rendements financiers quotidiens et estimons le manque à gagner prévu dans le cas de l'indice S&P 500 et de certaines actions de compagnies individuelles. La distribution généralisée est utilisée pour les innovations normalisées contenues dans un modèle asymétrique non linéaire de type GARCH. Les résultats démontrent de façon empirique l'utilité de la distribution généralisée pour améliorer les prévisions au sujet du risque de perte en cas de baisse du marché des actifs financiers.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2009s-24.

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Length: 19 pages
Date of creation: 01 May 2009
Date of revision:
Handle: RePEc:cir:cirwor:2009s-24
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  1. John Galbraith & Dongming Zhu, 2009. "A Generalized Asymmetric Student-T Distribution With Application To Financial Econometrics," Departmental Working Papers 2009-02, McGill University, Department of Economics.
  2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier.
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  8. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
  9. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the "t"-distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174.
  10. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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  12. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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