Journal of Risk Model Validation

Value-at-risk bounds for multivariate heavy tailed distribution: an application to the Glosten–Jagannathan–Runkle generalized autoregressive conditional heteroscedasticity model

Imed Gammoudi, Mohamed El Ghourabi and Lotfi Belkacem

  • Explicit VaR bounds for portfolios of possibly dependent financial assets are evaluated.
  • we propose to use EVT/GJR-GARCH combination to calculate a modified VaR where a shift of location is introduced. 
  • The proposed VaR has an interesting property of location invariance and take into consideration the different characteristics of financial data.
  • Empirical application and Backtesting procedure are used.


The aim of this paper is to derive value-at-risk (VaR) bounds for the portfolios of possibly dependent financial assets for heavy tailed Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroscedasticity processes using extreme value theory copulas. Using the 2014 contribution of Gammoudi et al made in "Value at risk estimation for heavy tailed distributions" as well as the 2005 paper by Mesfioui and Quessy titled "Bounds on the value-at-risk for the sum of possibly dependent risks", we provide modified VaR bounds for when a shift of location is introduced. These bounds have the interesting property of location invariance. Empirical studies for several market indexes are carried out to illustrate our approach.

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