1. Leveraging
Bad news – negative shocks – have a larger impact on volatility than good news or positive shocks.
This asymmetry is incorporated in a GARCH framework by the inclusion of a “leverage” effect.
Spring 2004
K. Ensor, STAT 421

2. Egarch
The exponential GARCH formulation models the log of the conditional variance as an ARMA structure with asymmetric innovations.
An advantage of modeling the “log” of the process – variances are guaranteed to be positive.
Spring 2004
K. Ensor, STAT 421

3. Egarch – the model (compare parameterization that of Splus)
Spring 2004
K. Ensor, STAT 421

4. Other variants – Splus documentation (Zivot)
Power GARCH – return to modeling the conditional variance.
Consider other behaviors the “squared GARCH behavior”.
Threshold GARCH – set a threshold for different models to kick in (leveraging is automatic).
Spring 2004
K. Ensor, STAT 421