Stochastic Volatility Models for Asset Returns with Leverage, Skewness and Heavy-Tails via Scale Mixture

We propose and estimate a new class of equity return models that incorporate scale mixtures of the skew-normal distribution for the error distribution into the standard stochastic volatility framework. The main advantage of our models is that they can simultaneously accommodate the skewness, heavy-tailedness, and leverage effect of equity index returns observed in the data. The proposed models are flexible and parsimonious, and include many asymmetrically heavy-tailed error distributions — such as skew-t and skew-slash distributions — as special cases. We estimate a variety of specifications of our models using the Bayesian Markov Chain Monte Carlo method, with data on daily returns of the S&P 500 index over 1987–2009. We find that the proposed models outperform existing ones of index returns.