Volatility Forecasting with SVD Derived Covariance Features: A Deep Learning Approach

Volatility forecasting remains a cornerstone of financial econometrics with applications in hedging, risk management, and asset allocation. While traditional models such as GARCH, HAR, and realized volatility frameworks capture temporal dependencies in single-asset volatility, they often fail to exploit information from the broader market’s cross-sectional structure. In contrast, the covariance matrix of asset returns encodes systemic co-movements that can serve as early indicators of market stress. Building on this insight, we propose a deep learning framework that enhances volatility prediction by integrating features derived from the singular value decomposition (SVD) of return covariance matrices. These features—such as the variance explained by leading principal components, generalized absorption ratios, and eigenvector alignment measures—capture the evolving interdependence and cohesion of financial markets. To ensure stability in high-dimensional settings, we estimate covariance matrices using Ledoit–Wolf shrinkage and feed the resulting SVD-based features, alongside traditional volatility predictors, into a neural network model. Empirical results on equity market data demonstrate that the proposed approach significantly outperforms benchmark models, including GARCH and HAR, in out-of-sample volatility forecasting. The findings highlight the predictive value of covariance-structure information and establish a pathway for combining market-wide factor dynamics with modern deep learning methods for improved volatility modeling. MSC Classification: 68T05 , 68T07 , 62P05