Regime Switching Stochastic Volatility with Skew, Fat Tails and Leverage using Returns and Realized Volatility Contemporaneously

A very general stochastic volatility (SV) model specification with leverage, heavy tails, skew and switching regimes is proposed, using realized volatility (RV) as an auxiliary time series to improve inference on latent volatility. The information content of the range and of implied volatility using the VIX index is also analyzed. Database is the S&P 500 index. Asymmetry in the observation error is modeled by the generalized hyperbolic skew Student-t distribution, whose heavy and light tail enable substantial skewness. Resulting number of regimes and dynamics differ dependent on the auxiliary volatility proxy and are investigated in-sample for the financial crash period 2008/09 in more detail. An out-of-sample study comparing predictive ability of various model variants for a calm and a volatile period yields insights about the gains on forecasting performance from different volatility proxies. Results indicate that including RV or the VIX pays off mostly in more volatile market conditions, whereas in calmer environments SV specifications using no auxiliary series outperform. The range as volatility proxy provides a superior in-sample fit, but its predictive performance is found to be weak.