Evaluation of volatility models for forecasting Value-at-Risk and Expected Shortfall in the Portuguese stock market

Abstract

We run a forecasting competition of different methodologies to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) with data on several stocks traded in the Euronext Lisbon stock exchange. The results are gauged using several backtesting procedures and compared with several loss functions. The asymmetric GARCH class with Extreme Value Theory generally performed better both for VaR and ES forecasting, especially, for more conservative coverage levels. Skewed distributions do not perform better than their conventional counterparts. The recommended sample size depends if the focus is on VaR or magnitude of the losses, although we find some superiority of larger sample sizes.