What good is a volatility model?

Abstract

A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylised facts about volatility that should be incorporated in a model; pronounced persistence and meanreversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility. We use data on the Dow Jones Industrial index to illustrate these stylised facts, and the ability of GARCH-type models to capture these features. We conclude with some challenges for future research in this area.