Stock-level volatility forecasting using machine learning: A comparative study of GARCH, Random Forest, LSTM, and GRU on US Equities

Forecasting stock price volatility at the individual stock level is a major challenge in managing financial risks; it has widespread implications for portfolio strategies, pricing derivatives, and assessing regulatory capital adequacy. Although there have been a number of studies using market indices (e.g., VIX and associated methods) to study forecasting stock market volatility, relatively few studies have applied and evaluated a number of different types of machine learning methods to individual stock data in terms of actual (realised) volatility forecasting. This study fills that gap by presenting a comprehensive analysis of the relationship between stock price volatility and various machine learning techniques on a sample of ten well-known US stocks (across three sectors: technology, finance, and energy) based on data from January 2018 to December 2024 (1,759 trading days). We apply five modelling approaches: a classical GARCH(1,1) econometric model, a classical GJR-GARCH(1,1,1) econometric model, a Random Forest regressor, a two-layer Long Short-Term Memory (LSTM) network, and a two-layer Gated Recurrent Unit (GRU) network. For each of the four modelling techniques, we use a rolling 5-day annualised actual (realised) volatility forecast as our final outcomes. Evaluation of the prediction results of each of these models was measured using RMSE, MAE, QLIKE loss, parametric Value-at-Risk (VaR) measures, Expected Shortfall (ES), and the Kupiec backtest. We also performed an analysis of the prevailing market regime through K-Means clustering, created an ablation study using variables as features in the models to assess the importance of those variables, and developed a computational efficiency benchmark for each model. In terms of predicted errors, Random Forest was proven to yield very low predicted error (mean RMSE = 0.0892) in comparison to deep learning methods, plus Random Forest was able to be trained approximately 7 times faster than deep learning methods. GRU was ranked second and outperformed LSTM on most of the metrics used in this evaluation. GARCH models remain a viable option for estimating risk measures and calibrating VaR, especially during period of stability in the financial markets.