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.