A value‐at‐risk computation based on heavy‐tailed distribution for dynamic conditional score models

The purpose of this study is to evaluate the estimating ability of GAS models in the computation of the value‐at‐risk by applying the extreme‐value theory. Our approach is the limiting result of an infinity shift of location. In this work, we use the generalized pareto distribution since it plays a central role in modelling heavy tail phenomena in many applications. A simulation study is performed to assess the estimated value‐at‐risk. Moreover, we examine the performance of the proposed method with daily returns of three stock market indices. The results prove that the presented approach gives good predictions for all indices.