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Alternative statistical distributions for estimating value-at-risk: theory and evidence

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  • Cheng-Few Lee

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  • Jung-Bin Su

    ()

Abstract

A number of applications presume that asset returns are normally distributed, even though they are widely known to be skewed leptokurtic and fat-tailed and excess kurtosis. This leads to the underestimation or overestimation of the true value-at-risk (VaR). This study utilizes a composite trapezoid rule, a numerical integral method, for estimating quantiles on the skewed generalized t distribution (SGT) which permits returns innovation to flexibly treat skewness, leptokurtosis and fat tails. Daily spot prices of the thirteen stock indices in North America, Europe and Asia provide data for examining the one-day-ahead VaR forecasting performance of the GARCH model with normal, student’s t and SGT distributions. Empirical results indicate that the SGT provides a good fit to the empirical distribution of the log-returns followed by student’s t and normal distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with SGT distributional setting, generates the most conservative VaR forecasts followed by student’s t and normal distributions for a long position. Consequently, it appears reasonable to conclude that, from the viewpoint of accuracy, the influence of both skewness and fat-tails effects (SGT) is more important than only the effect of fat-tails (student’s t) on VaR estimates in stock markets for a long position. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Cheng-Few Lee & Jung-Bin Su, 2012. "Alternative statistical distributions for estimating value-at-risk: theory and evidence," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 309-331, October.
  • Handle: RePEc:kap:rqfnac:v:39:y:2012:i:3:p:309-331 DOI: 10.1007/s11156-011-0256-x
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    References listed on IDEAS

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    1. So, Mike K.P. & Yu, Philip L.H., 2006. "Empirical analysis of GARCH models in value at risk estimation," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 16(2), pages 180-197, April.
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    Cited by:

    1. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo Group Munich.
    2. Su, Jung-Bin, 2014. "Empirical analysis of long memory, leverage, and distribution effects for stock market risk estimates," The North American Journal of Economics and Finance, Elsevier, vol. 30(C), pages 1-39.
    3. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    4. Su, Jung-Bin, 2015. "Value-at-risk estimates of the stock indices in developed and emerging markets including the spillover effects of currency market," Economic Modelling, Elsevier, vol. 46(C), pages 204-224.

    More about this item

    Keywords

    Value-at-risk; GARCH; SGT; Composite trapezoid rule; Quantile; C52; C53; G15;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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