Volatility Forecasting and Explanatory Variables: A Tractable Bayesian Approach to Stochastic Volatility

Abstract:     
We provide a formulation of stochastic volatility (SV) based on Gaussian process regression (GPR), a flexible framework for nonparametric Bayesian regression, applying it to the estimation and forecasting of asset price volatility processes. We show how GPR, in conjunction with range-based volatility measurements, allows for arbitrary covariates without having to specify a priori functional forms incorporating them. For out-of-sample forecasting of stock return volatility, this methodological contribution is supported by compelling empirical results. In a simulation analysis, we find that a GPR-based stochastic volatility (GPSV) model yields significantly more accurate forecasts, especially at long horizons, than SV and GARCH benchmarks. With actual market data, we confirm that the GPSV model significantly outperforms benchmarks at long horizons. Moreover, the GPSV model can straightforwardly account for macro-finance variables. When doing so, the improvements brought by the GPSV model are even more significant, at all horizons, from one-week- to one-year-ahead out-of-sample volatility forecasts. In particular, during the 2007-2009 recession, a GPSV model augmented with a simple set of exogenous variables yields a 26% reduction in error rate on one-year out-of-sample forecasting, compared with a benchmark range-based SV model.

Number of Pages in PDF File: 47

Keywords: Bayesian Volatility Models, Stochastic Volatility, Generalized Autoregressive Conditional Heteroscedasticity Models, Long Memory in Volatility, Multifactor Volatility

JEL Classification: C11, C22, C53

working papers series