Value at Risk Estimation for Heavy Tailed Distributions

The aim of this paper is to derive a coherent risk measure for heavy tailed GARCH processes using extreme value theory. For the proposed measure, the risk associated to a given portfolio is less than the sum of the stand-alone risks of its components. This measure which is value at risk (VaR), is the limiting result of an infinity shift of location and is less sensitive with respect to location change. Based on two international stock markets applications and an empirical backtesting procedure, the proposed VaR is found to be more accurate in all quantile levels.