Robust Bayesian Analysis of Heavy-tailed Stochastic Volatility Models using Scale Mixtures of Normal Distributions

This paper consider a Bayesian analysis of stochastic volatility models using a class of symmetric normal scale mixtures, which provides an appealing robust alternative to the routine use of the normal distribution in this type of models. Specific distributions examined include the normal, the Student-t, the slash and the variance gamma distribution which are obtained as a sub-class of our proposed class of models. Under a Bayesian paradigm, we explore an efficient Markov chain Monte Carlo (MCMC) algorithm for parameter estimation in this model. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify possible outliers. The methods developed are applied to analyze daily stock returns data on S\&P500 index. We conclude that our proposed rich class of normal scale mixture models provides an interesting robust alternative to the traditional normality assumptions often used to model thick-tailed stochastic volatility data.