Continuous time volatility modelling : COGARCH versus Ornstein-Uhlenbeck models

We compare the probabilistic properties of the non-Gaussian Ornstein-Uhlenbeck based stochastic volatility model of Barndorff-Nielsen and Shephard (2001) with those of the COGARCH process. The latter is a continuous time GARCH process introduced by the authors (2004). Many features are shown to be shared by both processes, but differences are pointed out as well. Furthermore, it is shown that the COGARCH process has Pareto like tails under weak regularity conditions. -- COGARCH ; continuous time GARCH ; GARCH ; generalised Ornstein-Uhlenbeck process ; L_evy process ; self-decomposable distribution ; stochastic volatility model ; tail behaviour