A comparative study of VaR and ES using extreme value theory

Abstract: Using data from OMXS30, we study which of the models block maxima and peaks-over-threshold, based on extreme value theory, are the most accurate when estimating the risk measures Value-at-Risk and Expected Shortfall. To perform this analysis, the risk measures are backtested. The extreme observations are fitted to the generalized extreme value distribution and the generalized Pareto distribution using maximum likelihood estimation. This study conclude that when estimating Value at Risk, block maxima is a more accurate model. When estimating Expected Shortfall, the difference between the models is not statistical significant.