■ GARCH Modeling of Stock Market Volatility
Previous authors have surveyed the econometric theory of GARCH (Engle, 1991; Bera and Higgins, 1993; Bollerslev et al., 1994; Bauwens et al., 2006; Teräsvirta, 2006; Silvennoinen and Teräsvirta, 2007) and their applications in financial markets (Bollerslev et al., 1992). In this chapter, we review the most commonly used univariate and multivariate GARCH models for stock market volatility. In so doing, we provide an easy-to-read, notationally consistent, and logically structured description of the most popular variants of the models, to guide financial analysts and researchers through the literature and help with the selection of the most appropriate variants for particular contexts. We begin in Section 4.2 by summarizing the essential characteristics of stock return volatilities that GARCH models should ideally capture. This serves as the benchmark to describe the basic univariate GARCH model and its many extensions. In Section 4.3, we review the important multivariate GARCH models. In Section 4.4, we discuss the most commonly used estimation procedures, and in Section 4.5 we review their applications in modeling stock market volatility. Our summary and conclusions are presented in Section 4.6.