Modeling conditional volatility using flexible smooth transition GARCH processes

Abstract

This paper develops a new asymmetric GARCH(l,l )process for modeling condi- tional volatility, whereby the ARCH parameter of GARCH(l,l)is replaced by a non- linear function of the lagged residuals and conditional volatility. This conditional

mode is estimated using several stock indices and individual stock returns. The empirical results show that the new asymmetric GARCH mode captures both sign and size asymmetries. Volatility responds stronger to large negative shocks than

to small negative s hocks, while large positive shocks lead to a reduction in volatil- ity. Moreover, the size asymmetry for positive shocks is stronger than for negative

shocks. In other words, sign asymmetry is substantially stronger for large shocks than for small shocks. The flexibility of the new model. is particular y important in modeling the dynamics of outliers. Unlike the behaviour in traditional GARCH models, the new model is consistent with volatility reverting to its normal value

very quickly after arge crashes.The results suggest that a pressure- re lief mecha- nism exists in most stock markets.