From a theoretical point of view, the selection of thresholds is a critical issue in the framework of the Peaks Over Threshold (POT) approach, which is why in the last decade numerous methodologies have been proposed for its selection. In this paper, we address this subject from an empirical point of view by assessing to what extent the selection of the threshold is decisive in quantifying the market risk. For measuring market risk, we use the Value at Risk (VaR) and the Expected Shortfall (ES) measures. The results obtained indicate that there is a large set of thresholds that provide similar Generalized Pareto Distribution (GPD) quantiles estimators and as a consequence similar market risk measures. Just only, for large thresholds, those corresponding to the 98th and 99th percentile of the GPD some differences are found. It means that the choice of threshold in the framework of the POT method may not be relevant in quantifying market risk when we use the VaR and ES measures for this task.
In this paper, we analyze the role of the heavy tail and skewed distribution in market risk estimation (Val ue at Risk (VaR)). In particular, we are interested in knowing if in the framework of the conditional extreme value theory, the estimation of the volatility model below heavy tail and skewed distribution contributes to improve the VaR estimation respect to these obtained from a symmetric distribution. The study has been carried out for six individual assets belonging to the digital sector: ADP, Amazon, Cerner, Apple, Microsoft and Telefonica. The analysis period runs from January 1st, 2008 to the end of December 2013. Although the evidence found is a little bit weak, the results obtained seem to indicate that the heavy tail and skewed distribution outperforms the symmetric distribution both in terms of accuracy VaR estimations as in terms of firm's loss func tion. Furthermore, the market risk capital requirements fixed on the base of the VaR estimations are also lowest below a skewed distribution.JEL Classifications: C15, C22, C52, G17, G32.
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