Estimating a semiparametric asymmetric stochastic volatility model with a dirichlet process mixture

Abstract. This paper extends the stochastic volatility with leverage model, where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparamet-rically. The novelty of the paper is in modeling the unknown distribution with an infinite ordered mixture of bivariate normals with mean zero, but whose mixture probabilities and covariance matrices are unknown and modeled with the Dirichlet Process prior. A Bayesian Markov chain Monte Carlo sampler is designed to fully characterize the parametric and distributional uncertainty. Cumulative marginal likelihoods and log predictive Bayes factors for the semiparametric and parametric asymmetric stochastic volatility models are compared. We find substantial empirical evidence in favor of the semiparametric leverage version of the stochastic volatility model