I have been using various GARCH-based models to forecast volatility for various North American equities using historical daily data as inputs.
Asymmetric GARCH models are often cited as a modification of the basic GARCH model to account for the 'leverage effect' i.e. volatility tends to increase more after a negative return than a similarly sized positive return.
What kind of a difference would you expect to see between a standard GARCH and an asymmetric GARCH forecast for a broad-based equity index like the S&P 500 or the NASDAQ-100?
There is nothing particularly special about these two indices, but I think it is helpful to give something concrete to focus the discussion, as I am sure the effect would be different depending on the equities used.