There are numerous extensions to the GARCH framework. Some popular models include:

• GJR-GARCH: A variant of the GARCH model that takes into account the asymmetry of the returns (negative returns tend to have a stronger impact on volatility than positive ones)
• EGARCH: Exponential GARCH
• TGARCH: Threshold GARCH
• FIGARCH: Fractionally integrated GARCH, used with non-stationary data
• GARCH-MIDAS: In this class of models, volatility is decomposed into a short-term GARCH component and a long-term component driven by an additional explanatory variable
• Multivariate GARCH models, such as CCC-/DCC-GARCH

The first three models use slightly different approaches to introduce asymmetry into the conditional volatility specification. This is in line with the belief that negative shocks have a stronger impact on volatility than positive shocks.