Backtesting expected shortfall for world stock indexETFswith extreme value theory andGram-Charliermixtures

This paper analyses risk quantification for three main stock market index exchange-traded funds in world financial markets. We compare the relative performance of a set of parametric and semi-nonparametric models in terms of both value-at-risk and expected shortfall backtesting techniques. To this end, we explore the result of the jointly elicitability of these two risk measures. We provide a new mixture of Gram-Charlier distributions that have been used in this framework for the first time and derive a close formula for directly computing expected shortfall. This model is compared to the Gaussian (benchmark model), Student'st, generalized Pareto (a case of the extreme value theory) and mixtures of Gram-Charlier distributions. The results show that peaks-over-threshold (extreme value theory) and flexible Gram-Charlier approximations are suitable to quantify market risk and mitigate concerns about possible financial instabilities generated by misuse of exchange-traded funds trading.

Automated summary

The paper analyzes risk quantification for three main stock market index exchange-traded funds in world financial markets, comparing parametric and semi-nonparametric models. The study shows that peaks-over-threshold and flexible Gram-Charlier approximations are suitable for quantifying market risk.