Tree-Based Methods of Volatility Prediction for the S&P 500 Index

Abstract

Predicting asset return volatility is one of the central problems in quantitative finance. These predictions are used for portfolio construction, calculation of value at risk (VaR), and pricing of derivatives such as options. Classical methods of volatility prediction utilize historical returns data and include the exponentially weighted moving average (EWMA) and generalized autoregressive conditional heteroskedasticity (GARCH). These approaches have shown significantly higher rates of predictive accuracy than corresponding methods of return forecasting, but they still have vast room for improvement. In this paper, we propose and test several methods of volatility forecasting on the S&P 500 Index using tree ensembles from machine learning, namely random forest and gradient boosting. We show that these methods generally outperform the classical approaches across a variety of metrics on out-of-sample data. Finally, we use the unique properties of tree-based ensembles to assess what data can be particularly useful in predicting asset return volatility.

Keywords

• volatility
• tree ensembles
• GARCH
• prediction
• machine learning