Volatility specifications versus probability distributions in VaR forecasting

We provide evidence suggesting that the assumption on the probability distribution for return in- novations is more influential for Value at Risk (VaR) performance than the conditional volatility specification. We also show that some recently proposed asymmetric probability distributions and the APARCH and FGARCH volatility specifications beat more standard alternatives for VaR fore- casting, and they should be preferred when estimating tail risk. The flexibility of the free power parameter in conditional volatility in the APARCH and FGARCH models explains their better performance. Indeed, our estimates suggest that for a number of financial assets, the dynamics of volatility should be specified in terms of the conditional standard deviation. We draw our results on VaR forecasting performance from i) a variety of backtesting approaches, ii) the Model Confi- dence Set approach, as well as iii) establishing a ranking among alternative VaR models using a precedence criterion that we introduce in this paper.