Backtesting Extreme Value Theory Models of Expected Shortfall

Abstract

We use stock market data to analyze the quality of alternative models and procedures to estimate Expected Shortfall (ES) at different significance levels. We consider conditional models applied to the full distribution of returns as well as models that focus on tail events using extreme value theory (EVT) under the two-step procedure proposed by McNeil&Frey (2000). The performance of the different models is assessed using a variety of ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1- and 10-day ES forecasts than non-EVT based models. Under either approach, asymmetric probability distributions for return innovations are clearly more appropriate. These qualitative results are also valid for the recent crisis period, even though all models then undervalue the level of risk. Filtered Historic Simulation narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be the best approach to obtain accurate ES forecasts.