Bayesian nonparametric modeling of stochastic volatility

This paper introduces a novel discrete-time stochastic volatility model that employs a countably infinite mix- ture of AR(1) processes, with a Dirichlet process prior, to nonparametrically model the latent volatility. Realized variance (RV) is incorporated as an ex post signal to enhance volatility estimation. The model effectively cap- tures fat tails and asymmetry in both return and log(RV) conditional distributions. Empirical analysis of three major stock indices provides strong evidence supporting the nonparametric stochastic volatility. The results re- veal that the volatility equation components exhibit significant variation over time, enabling the estimation of a more dynamic volatility process that better accommodates extreme returns and variance shocks. The new model delivers out-of-sample density forecasts with strong evidence of improvement, particularly for returns, log(RV), and the left region of the return distribution, including negative returns and extreme movements below −1% and −2%. The new approach provides improvements in forecasting the tail-risk measures of value-at-risk and expected shortfall.