Gaussian Processes and Non-parametric Volatility Forecasting

We provide a formulation of stochastic volatility based on Gaussian processes, a flexible framework for Bayesian nonlinear regression. The advantage of using Gaussian processes in this context is to place volatility forecastingwithin a regression framework; this allows a large number of explanatory variables to be used for forecasting, a task difficult with standard volatility-forecasting formulations. Our approach builds upon the range-based estimator of Alizadeh, Brandt, and Diebold (2002) to provide much greater accuracy than traditional close-to-close estimators using daily data. Experiments with high-frequency stock market data, using five-minute realized volatility as a benchmark, show that the approach significantly outperforms standard stochastic volatility and GARCH models in one-month-ahead out-of-sample volatility forecasting. It also shows promise for long-range (several months ahead) forecasting, an application that could prove useful in pricing long-dated options.