Analysis of stock market volatility by continuous-time GARCH models

Understanding the volatility of a market is critical to our understanding of finance. The returns of an equity market as a whole-where the market’s returns may be proxied, for example, by the returns on an index such as the S and P500 index-are frequently modeled as a function of investors’ expectations of the market’s volatility (see, for example, Merton, 1980; French et al., 1987; Abel, 1988; Barsky, 1989). Ang et al. (2006) present evidence that the volatility of the market is a candidate for inclusion as an additional factor augmenting standard multifactor models of the cross section of stock returns (Fama and French, 1993; Carhart, 1997). In arguing that total risk is priced, Ang et al. (2006) present a considerable challenge to paradigms that argue that only diversifiable, or systematic, risk is required to capture the cross section of expected equity returns (Sharpe, 1964).