An empirical review of dynamic extreme value models for forecasting value at risk, expected shortfall and expectile

Abstract

This work provides a selective review of the most recent dynamic models based on extreme value theory, in terms of their ability to forecast financial losses through different risk measures. The main characteristic of these models is that their dynamics depend only on the occurrence and magnitude of extreme events above a high threshold. Through an empirical analysis, we evaluate the predictive ability of these approaches on a set of stock market indices. In an in-sample analysis, we assess the goodness-of-fit of the different specifications. We also compare the adequacy of each model, considering how well they forecast the risk measures in the out-of-sample period. In addition, in order to identify the best-performing models, we use the model confident set procedure across different risk measures, loss functions, and score functions to identify the superior models. Finally, we identify some potential avenues for future research.