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Forecasting Expected Shortfall With A Generalized Asymmetric Student-T Distribution

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Author Info
John Galbraith ()
Dongming Zhu ()

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Abstract

Financial returns typically display heavy tails and some skewness, and cinditional vairance 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 composite index; 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.

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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2009-01.

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Length: 14 pages
Date of creation: Jan 2009
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Handle: RePEc:mcl:mclwop:2009-01

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

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  3. Dima Alberg & Haim Shalit & Rami Yosef, 2008. "Estimating stock market volatility using asymmetric GARCH models," Applied Financial Economics, Taylor and Francis Journals, vol. 18(15), pages 1201-1208. [Downloadable!] (restricted)
  4. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August. [Downloadable!] (restricted)
  5. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309. [Downloadable!] (restricted)
  6. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October. [Downloadable!] (restricted)
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  8. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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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. [Downloadable!]
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