Modelling daily value-at-risk using realized volatility and arch type models

In this paper we show how to compute a daily VaR measure for two stock indexes (CAC40 and SP500) using the one-day-ahead forecast of the daily realized volatility. The daily re-alized volatility is equal to the sum of the squared intraday returns over a given day and thus uses intraday information to define an aggregated daily volatility measure. While the VaR specification based on an ARFIMAX(0,d,1)-skewed Student model for the daily realized volatility provides adequate one-day-ahead VaR forecasts, it does not really improve on the performance of a VaR model based on the skewed Student APARCH model and estimated using daily data. Thus, for the two financial assets considered in an univariate framework, both methods seem to be equivalent. This paper also shows that daily returns standardized by the square root of the one-day-ahead forecast of the daily realized volatility are not normally distributed.