In the prediction of quantiles of daily Standard&Poor’s 500 (S&P 500) returns we consider how to use high-frequency 5-minute data. We examine methods that incorporate the high frequency information either indirectly, through combining forecasts (using forecasts generated from returns sampled...

We develop the analytical second-order bias of a Value-at-Risk estimator based on an ARCH(1) volatility specification when the parameters are estimated by the method of quasi maximum likelihood. We show that the bias results from two sources: assumption on the distribution of the standardized...

We investigate the predictive performance of various classes of value-at-risk (VaR) models in several dimensions — unfiltered versus filtered VaR models, parametric versus nonparametric distributions, conventional versus extreme value distributions, and quantile regression versus inverting the...