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Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution

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  • Dongming Zhu
  • John W. Galbraith

Abstract

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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  • Dongming Zhu & John W. Galbraith, 2009. "Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution," CIRANO Working Papers 2009s-24, CIRANO.
    • Handle: RePEc:cir:cirwor:2009s-24
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    Cited by:

    1. Saissi Hassani, Samir & Dionne, Georges, 2023. "Using skewed exponential power mixture for VaR and CVaR forecasts to comply with market risk regulation," Working Papers 23-2, HEC Montreal, Canada Research Chair in Risk Management.
    2. Kumiega, Andrew & Neururer, Thaddeus & Van Vliet, Ben, 2011. "Independent component analysis for realized volatility: Analysis of the stock market crash of 2008," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(3), pages 292-302, June.
    3. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3498-3516.
    4. Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
    5. Richard Gerlach & Zudi Lu & Hai Huang, 2013. "Exponentially Smoothing the Skewed Laplace Distribution for Value‐at‐Risk Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 534-550, September.

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    More about this item

    Keywords

    asymmetric distribution; expected shortfall; NGARCH model; distribution asymétrique; manque à gagner prévu; modèle NGARCH (Nonlinear Generalized AutoRegressive Conditional Heteroscedasticity);
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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