Contemporaneous asymmetry in GARCH processes

The paper introduces a new concept of asymmetry (contemporaneous asymmetry) in conditional heteroskedasticity models. We propose an original class of models aimed to capture the leverage effect, contemporaneous asymmetry as well as time-varying skewness and kurtosis. Not only past up and down moves have different impacts on the conditional variance, but also, positive and negative changes are governed by different conditional variances. We give conditions for the existence of a second-order and strictly stationary solution. The paper also provides consistency results on the quasi-maximum likelihood estimation. Finally, an empirical analysis on the French CAC 40 stock index is proposed.