Simulation and inference for stochastic volatility models driven by Lévy processes

We extend the currently most popular models for the volatility of financial time se-ries, Ornstein-Uhlenbeck stochastic processes, to more general non Ornstein-Uhlenbeck models. In particular, we investigate means of making the correlation structure in the volatility process more flexible. For one model, we implement a method for introducing quasi long-memory into the volatility model. We demonstrate that the models can be fitted to real share price returns data, and that results indicate that for the series we study, the long-memory aspect of the model is not supported. Some key words: Volatility; Long-memory; Fractional Ornstein-Uhlenbeck Process; Power decay proces