Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects

This paper extends the multiscale stochastic volatility (MSSV) models to allow for heavy tails of the marginal distribution of the asset returns and correlation between the innovation of the mean equation and the innovations of the latent factor processes. Novel algorithms of Markov Chain Monte Carlo (MCMC) are developed to estimate parameters of these models. Results of simulation studies suggest that our proposed models and corresponding estimation methodology perform quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample volatility forecasts of the fitted models. In addition the models and MCMC methods are applied to data sets of asset returns from both foreign currency and equity markets