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High-order moments and extreme value approach for value-at-risk

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  • Lin, Chu-Hsiung
  • Changchien, Chang-Cheng
  • Kao, Tzu-Chuan
  • Kao, Wei-Shun

Abstract

We modify a two-step approach by McNeil and Frey (2000) for forecasting Value-at-Risk (VaR). Our approach combines the asymmetric GARCH (GJR) model that allows the high-order moments (i.e., skewness and kurtosis) of the skewed generalized t (SGT) distribution to rely on the past information set to estimate volatility, and the modified Hill estimator (Huisman et al., 2001) for estimating the innovation distribution tail of the GJR model. Using back-testing of the daily return series of 10 stock markets, the empirical results show that our proposed approach could give better one-day VaR forecasts than McNeil and Frey (2000) and the GJR/GARCH models with alternative distributions. In addition, our proposed approach also provides the accuracy of expected shortfall estimates. The evidence demonstrates that our proposed two-step approach that incorporates the modified Hill estimator into the GJR model based on the SGT density with autoregressive conditional skewness and kurtosis provides consistently accurate VaR forecasts in the short and longer sample periods.

Suggested Citation

  • Lin, Chu-Hsiung & Changchien, Chang-Cheng & Kao, Tzu-Chuan & Kao, Wei-Shun, 2014. "High-order moments and extreme value approach for value-at-risk," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 421-434.
  • Handle: RePEc:eee:empfin:v:29:y:2014:i:c:p:421-434
    DOI: 10.1016/j.jempfin.2014.10.001
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    References listed on IDEAS

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    Keywords

    Value-at-Risk; Skewed generalized t distribution; Extreme value theory; Tail-index; VaR-x method;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • F37 - International Economics - - International Finance - - - International Finance Forecasting and Simulation: Models and Applications

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