Bayesian nonparametric modelling of stochastic volatility

This paper introduces a novel discrete-time stochastic volatility model that employs a countably infinite mixture 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 captures 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 reveal 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\% $ −1% and $ -2\% $ −2%. The new approach provides improvements in forecasting the tail-risk measures of value-at-risk and expected shortfall.