Asymmetric ARCH models

The feature of capturing the volatility clustering in asset returns has made (G)ARCH
models very popular in empirical studies. Nevertheless, these models are subject to
limitations. Empirical studies have observed that stock returns are negatively related
with changes in return volatility. Volatility tends to rise when prices are falling, and
to fall when prices are rising. Hence, the existence of asymmetry in volatility, which
is often referred to as the leverage effect. All the models described in the previous
section assumed that only the magnitude and not the sign of past returns determines
the characteristics of the conditional variance, ht . In other words, the ARCH and
GARCH models described earlier do not discriminate negative from positive shocks
which has been shown to have differing impacts on the conditional variance.