Beyond GARCH: Bayesian Neural Stochastic Volatility

Accurately forecasting volatility is central to risk management, portfolio allocation, and asset pricing. While high-frequency realised measures have been shown to improve predictive accuracy, their value is not uniform across markets or horizons. This paper introduces a class of Bayesian neural network stochastic volatility (NN-SV) models that combine the flexibility of machine learning with the structure of stochastic volatility models. The specifications incorporate realised variance, jump variation, and semivariance from daily and intraday data, and model uncertainty is addressed through a Bayesian stacking ensemble that adaptively aggregates predictive distributions. Using data from the DAX, FTSE 100, and S&P 500 indices, the models are evaluated against classical GARCH and parametric SV benchmarks. The results show that the predictive content of high-frequency measures is horizon- and market-specific. The Bayesian ensemble further enhances robustness by exploiting complementary model strengths. Overall, NN-SV models not only outperform established benchmarks in many settings but also provide new insights into market-specific drivers of volatility dynamics.