Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes

This paper discusses Bayesian inference for stochastic volatility models based on continuous superpositions of Ornstein-Uhlenbeck processes. These processes represent an alternative to the previously considered discrete superpositions. An interesting class of continuous superpositions is defined by a Gamma mixing distribution which can define long memory processes. We develop efficient Markov chain Monte Carlo methods which allow the estimation of such models with leverage effects. This model is compared with a two-component superposition on the daily Standard and Poor’s 500 index from 1980 to 2000. ∗Corresponding author: Jim Griffin, Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, U.K. Tel.: +44-1227-823627; Fax: +44-1227-827932; Email: [email protected].