Particle filtering of stochastic volatility modeled with leverage

In this paper, we address univariate stochastic volatility models that allow for correlation of the perturbations in the state and observation equations, i.e., models with leverage. We propose a particle filtering method for estimating the posterior distributions of the log-volatility, where we employ Rao-Blackwellization of the unknown static parameters of the model. We also propose a scheme for choosing the best model from a set of considered models and a test for assessing the validity of the selected model. We demonstrate the performance of the proposed method on simulated and S&P 500 data.