Bayesian inference for Heston-STAR models

The Heston-STAR model is a new class of stochastic volatility models defined by generalizing the Heston model to allow the volatility of the volatility process as well as the correlation between asset log-returns and variance shocks to change across different regimes via smooth transition autoregressive (STAR) functions. The form of the STAR functions is very flexible, much more so than the functions introduced in Jones (J Econom 116:181–224, 2003), and provides the framework for a wide range of stochastic volatility models. A Bayesian inference approach using data augmentation techniques is used for the parameters of our model. We also explore goodness of fit of our Heston-STAR model. Our analysis of the S&P 500 and VIX index demonstrates that the Heston-STAR model is more capable of dealing with large market fluctuations (such as in 2008) compared to the standard Heston model.