Comparison of the accuracy of models in forecasting VAR and ES Through time

Abstract

Purpose- Identify the best model/method to accurately forecast the Value-at-Risk (VaR) and the Expected Shortfall (ES) of position. Methodology- The dynamic of each retained return series was estimated with one of retained GARCH-type model combined with one of retained probability distributions (normal, fat-tailed, and skewed) in each retained sub-periods (window). In each window (sub-period), the 1-day ahead VaR and ES were forecasted by using the best selected GARCH-type model. More than 4000 1-day ahead VaR and ES were forecasted with each retained model/method. Based on 252-day rolling-window, forecasted VaR and ES with each retained model/method were backtested around 3750 times. Findings- Our results revealed that the best fitting GARCH-specifications combined with skewed Student or GED distribution enable to accurately forecast VaR more often. However, the best methods based on the best fitting GARCH-specifications combined with the best fitting probability distribution do not improve the frequency of acceptance of the null hypothesis stating the accuracy of the method. The accuracy of models tends to deteriorate during crises periods. Conclusion- Modeling and forecasting the dynamic of retained series with skewed probability distributions (skwed student or wked GED) improve the forecasting accuracy of a parametric or semi parametric model. A performan model in sample may not perform well out sample. Forecasted VaR should be complemented with Stressed VaR or ES. Keywords: VaR, ES, parametric, semi-parametric, backtesting, probability distribution, rolling-window. JEL Codes: G11, C10, C51