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Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures

Author

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  • Fabrizio Laurini
  • Jonathan Tawn

Abstract

Stock returns exhibit heavy tails and volatility clustering. These features, motivating the use of GARCH models, make it difficult to predict times and sizes of losses that might occur. Estimation of losses, like the Value-at-Risk, often assume that returns, normalized by the level of volatility, are Gaussian. Often under ARMA-GARCH modeling, such scaled returns are heavy tailed and show extremal dependence, whose strength reduces when increasing extreme levels. We model heavy tails of scaled returns with generalized Pareto distributions, while extremal dependence can be reduced by declustering data.

Suggested Citation

  • Fabrizio Laurini & Jonathan Tawn, 2009. "Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 146-169.
    • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:146-169
    DOI: 10.1080/07474930802387985
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    Cited by:

    1. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
    2. Zhang, Zhengjun & Zhu, Bin, 2016. "Copula structured M4 processes with application to high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 231-241.
    3. Zhao, Zifeng & Zhang, Zhengjun & Chen, Rong, 2018. "Modeling maxima with autoregressive conditional Fréchet model," Journal of Econometrics, Elsevier, vol. 207(2), pages 325-351.

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