index returns. The proposed models capture key stylized facts of such returns, namely heavy tails, asymmetry, volatility … asymmetric. Volatility is modeled parametrically. The new model is applied to the daily returns of the S\&P 500, FTSE 100, and … EUROSTOXX 50 indices and is compared to GARCH, Stochastic Volatility, and other Bayesian semi-parametric models …