Annual VaR from High Frequency Data

We study the properties of dynamic models for realized variance on long term VaR analyzing the density of future Integrated Variance. Mixing this density with the conditional density of returns given the volatility we derive the predictive density of returns, which we use to estimate VaR. We find that dynamic specifications characterized by higher persistence lead to more conservative VaR estimates when longer horizons are considered. We compare our long term VaR estimates to the ones obtained using the square root of time rule. We show that this scaling rule works approximately well.