COGARCH processes: theory and asymptotics for the pseudo-maximum likelihood estimator

COGARCH processes are Lévy driven continuous time version of well known GARCH models for modeling high-fequency financial returns. We firstly discuss the properties about Lévy processes such as symmetric and asymmetric COGARCH models. These results are prerequisites to draw statistical inference from irregularly spaced observations. In particular, we focus on the pseudo-maximum likelihood method in order to extend some asymptotic results to the asymmetric model.