This paper is concerned with simulation-based inference in generalized models of stochastic volatility deÿned by heavy-tailed Student-t distributions (with unknown degrees of freedom) and exogenous variables in the observation and volatility equations and a jump component in the observation equation. By building on the work of Kim, Shephard and Chib (Rev. Econom. Stud. 65 (1998) 361), we develop e cient Markov chain Monte Carlo algorithms for estimating these models. The paper also discusses

more »

... the likelihood function of these models can be computed by appropriate particle ÿlter methods. Computation of the marginal likelihood by the method of Chib (J. Amer. Statist. Assoc. 90 (1995) 1313) is also considered. The methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the S&P 500 index where several stochastic volatility models are formally compared under di erent priors on the parameters.