A new approach to model and forecast volatility based on extreme value of asset prices

Based on the specification of the Conditional Autoregressive Range (CARR) model, we provide a framework that makes use of volatility based on the high and the low of daily prices separately to model the dynamic behavior of the conditional Rogers and Satchell (1991) estimator called herein the Conditional Autoregressive Rogers and Satchell (CARRS) model. We assess the performance of the CARRS model for forecasting daily realized volatility (estimated based on high frequency data) using loss functions, the regression test and the superior predictive ability test and compare them with forecasting performance of alternative models. Our results indicate that the CARRS model exhibits superior forecasting performance when compared to alternative models.