Stochastic volatility models with leverage and heavy-tailed distributions: A Bayesian approach using scale mixtures

Abstract

This paper studies a heavy-tailed stochastic volatility (SV) model with leverage effect, where a bivariate Student- t distribution is used to model the error innovations of the return and volatility equations. Choy et al. (2008) studied this model by expressing the bivariate Student- t distribution as a scale mixture of bivariate normal distributions. We propose an alternative formulation by first deriving a conditional Student- t distribution for the return and a marginal Student- t distribution for the log-volatility and then express these two Student- t distributions as a scale mixture of normal (SMN) distributions. Our approach separates the sources of outliers and allows for distinguishing between outliers generated by the return process or by the volatility process, and hence is an improvement over the approach of Choy et al. (2008). In addition, it allows an efficient model implementation using the WinBUGS software. A simulation study is conducted to assess the performance of the proposed approach and its comparison with the approach by Choy et al. (2008). In the empirical study, daily exchange rate returns of the Australian dollar to various currencies and daily stock market index returns of various international stock markets are analysed. Model comparison relies on the Deviance Information Criterion and convergence diagnostic is monitored by Geweke’s convergence test.