Higher moments for the Cogarch(1,1) model

The COGARCH (COntinuous Generalized Auto-Regressive Conditional Heteroschedastic) model can be considered as a continuous version of the well known GARCH discrete time model. They are driven by general L evy processes and the resulting volatility process satis es a stochastic di erential equation. The main di erence between COGARCH models and other stochastic volatility models is that there is only one source of randomness (the L evy process) and all the stylized feature are captured by the dependance structure of the model as in the GARCH models. A general method to calculate the moment of higher order of the COGARCH(1,1) model is presented. A general formula to calculate all the joint and the conditional moments is also provided. The explicit form of the higher moment is useful to apply some prediction based estimation function (PBEF) methods to estimate the parameters of the COGARCH models and in particular to find an optimal PBEF.