Sequential Monte Carlo Methods for stochastic volatility models with jumps

In this paper we propose a sequential Monte Carlo algorithm to estimate a stochastic volatility model with leverage effect, non constant conditional mean and jumps. Our idea relies on the auxiliary particle filter algorithm together with the Markov Chain Monte Carlo (MCMC) methodology. Our method allows to sequentially evaluate the parameters and the latent processes involved in the dynamics of interest. An empirical application on simulated data and on the Standard & Poor's 500 index is presented to study the performance of the algorithm implemented.