George Dotsis, Raphael N. Markellos and Terence C. Mills 9530.08000.06000.04000.02000.0000–0.0200–0.0400–0.0600–0.0800Figure 19.1 Logarithmic returns of the S&P500 over the period January 2, 1990, to December
31, 2007
- Leverage effect. Stock returns are negatively correlated with volatility, a phe-
nomenon which Black (1976) coined the “leverage effect.” When the stock
price of a firm declines the leverage of the firm increases and hence the firm’s
price becomes more risky and volatile. Modified GARCH processes, such as the
threshold-GARCH (TGARCH) model of Glosten, Jagannathan and Runkle (1993)
and the exponential-GARCH (EGARCH) model of Nelson (1991), are designed to
capture this leverage effect. However, many studies have shown that the asym-
metric relationship between asset returns and volatility cannot be explained
solely by leverage (for example, see Black, 1976; Christie, 1982; Schwert,
1989). - Information arrivals. Information arrival is non-uniform through time. Clark
(1973) linked asset returns to the arrival of information and was one of the
first examples of stochastic volatility. The intuition here is that, when infor-
mation arrival is non-uniform, randomness in business activity can generate
randomness in volatility. Easley and O’Hara (1992) developed a market-
microstructure model with time deformation that provided, amongst other
things, a direct link between market volatility, trading volume and quote
arrivals. In continuous-time finance there is a large literature that allows ran-
domness in business time by using time-changed Lévy processes, which can
generate stochastic volatility, fat tails and leverage effects (for example, Carr
and Wu, 2004). - Volatility dynamics. Stochastic volatility is usually assumed to follow a mean
reverting process. Mean reversion in volatility is consistent with the cluster-
ing phenomenon and is also consistent with the economic interpretation of
volatility as a measure of risk. It implies that volatility oscillates around a long
run mean according to the speed with which it reverts to this mean level. The