Hierarchical Machine Learning for Variance Risk Premium Estimation: From VIX Forecasting to Options Trading
Hierarchical Machine Learning for Variance Risk Premium Estimation: From VIX Forecasting to Options Trading
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Original abstract
<div> The variance risk premium is the persistent wedge between implied and realised volatility. It represents one of the most economically significant risk premia in finan-cial markets. This dissertation develops a hierarchical machine learning framework for estimating and exploiting the variance risk premium through systematic options trading on the S&P 500. Rather than forecasting the VRP directly, the proposed ar-chitecture decomposes the problem into two parallel forecasting tasks, next-day VIX prediction using XGBoost regression on AR(1) residuals, and 22-day-ahead realised volatility prediction using a separate XGBoost model trained on OHLC data. The VRP forecast is then constructed by combining these component predictions, en-abling transparent error attribution and modular model improvement. </div> <div> Using daily data spanning January 1990 to February 2026, which encompasses the dot-com bubble, the Global Financial Crisis, and the COVID-19 pandemic this study evaluates the XGBoost framework against standard econometric models in-cluding HAR and GARCH models. </div> <div> For realised volatility, a comparison of five daily variance estimators including close-to-close, Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang demon-strates that range-based estimators achieve up to 2.46 times the statistical efficiency of close-to-close returns. </div> <div> The dissertation contributes an AR(1)-residual XGBoost framing that isolates the nonlinear signal from the dominant autoregressive component, a multi-estimator realised volatility pipeline, a hierarchical VRP prediction architecture with formal error decomposition, and comprehensive regime-conditional evaluation across low, medium, and high volatility environments. The framework provides a foundation for systematic VRP harvesting strategies in the S&P 500 options market, while high-lighting the fundamental challenge of horizon mismatch in combining one-step-ahead VIX forecasts with multi-step RV predictions. </div>