Simulation and inference for stochastic volatility models driven by Lévy processes

Abstract

We study Ornstein-Uhlenbeck stochastic processes driven by Lévy processes, and extend them to more general non-Ornstein-Uhlenbeck models. In particular, we investigate the 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.