Keywords: APARCH (Asymmetric Power ARCH), Asymmetries, EGARCH (Exponential GARCH), Ergodicity, GJR-GARCH, Kurtosis, Leverage effect, Moments, News Impact Curve, QGARCH (Quadratic GARCH), Stationarity, TGARCH (Threshold GARCH), Top Lyapounov's Exponent.
Description: Classical GARCH models, studied in the first two parts, rely on modeling the conditional variance conditionnelle as a linear function of the squared past innovations. The merits of this specification are its ability to reproduce several important characteristics of financial time series - succession of quiet and turbulent periods, autocorrelation of the squares but absence of autocorrelation of the returns, leptokurticity of the marginal distributions - and the fact that it is sufficiently simple to allow for an extended study of the probability and statistical properties. From en empirical point of view, however, the classical GARCH modeling has an important drawback. Indeed, by construction, the conditional variance only depends on the module of the past variables: past positive and negative innovations have the same effect on the current volatility. This property is in contradiction with many empirical studies on series of stocks, showing a negative correlation between the squared current innovation and the past innovations: if the conditional distribution was symmetric in the past variables, such a correlation would be equal to zero. On the contrary, conditional asymmetry is a stylized fact: the volatility increase due to a price decrease is generally stronger than that resulting from a price increase of the same magnitude.