Seasonal asymmetric persistence in volatility: an extension of GARCH models

In this paper, we study non-linear dynamics in the CAC 40 stock index. Our empirical results, suggest combining seasonality, persistence and asymmetric effects to model the conditional volatility. We observe that seasonality can have an asymmetric impact on the volatility. In particular, we show that negative shocks observed on Mondays have a greater impact on the volatility than the other days. Then we construct a seasonal asymmetric GARCH model. It consists to add seasonal terms in the variance equation of a GJR-GARCH (1,1) model.