Conditional Heteroskedasticity of Return Range Processes

Abstract: Price range contains important information about the asset volatility, and has long been considered an important indicator for it. In this paper, we propose to jointly model the [low, high] price range as a random interval and introduce an interval-valued GARCH (Int-GARCH) model for the corresponding [low, high] return range process. Model properties are presented under the general framework of random sets, and the parameters are estimated by a metric-based conditional least squares (CLS) method. Our empirical analysis of the daily return range data of Dow Jones component stocks yields very interesting results.