Capturing Heterogeneity: Machine Learning Approaches to Implied Volatility Forecasting

Despite documented heterogeneity in volatility dynamics across the option surface, standard implied volatility forecasting models apply homogeneous parameters throughout. We introduce a machine-learning framework that uses regression trees to partition the surface along both moneyness and maturity dimensions, identifying data-driven regions where distinct forecasting models perform best. Extending the Surface Heterogeneous Autoregressive (SHAR) framework of Dufays, Jacobs, and Rombouts (2025), we develop tree-based SHAR specifications that preserve interpretable structure while allowing model parameters to vary across the surface. Empirical analysis using S&P 500 options demonstrates that the boosted tree-based specification achieves the lowest out-of-sample forecast errors across all horizons, reducing one-month-ahead RMSE by 13 percent versus the benchmark SHAR model. The improvements are statistically significant and particularly pronounced during stress periods. The estimated tree presents economically interpretable segmentation: short-dated options exhibit higher daily persistence but lower monthly persistence than long-dated options, while deep out-of-the-money calls or puts display distinct dynamics from near-the-money contracts.