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

- We provide a framework based on an extension of the CARR model of Chou (2005).
- We model the conditional volatility based on the high and low prices separately.
- The conditional RS estimator is the average of the high and the low estimates.
- The CARRS model can effectively capture the dynamics of conditional volatility.
- The CARRS model provides better out-of-sample forecasts relative to GARCH models.

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.