Deep Learning Enhanced Multivariate GARCH

Abstract

This thesis develops a unified multivariate volatility modeling framework that integrates deep learning architectures into multivariate GARCH processes. Beginning with the Long Short-Term Memory enhanced BEKK (LSTM-BEKK) model, the study combines the flexibility of recurrent neural networks with the econometric interpretability of BEKK to capture nonlinear, dynamic, and high-dimensional dependence structures in financial return data. The model effectively overcomes key limitations of traditional MGARCH frameworks, such as their restricted ability to represent persistent volatility clustering and asymmetric co-movements. Empirical analyses across multiple equity markets show that the LSTM-BEKK model significantly improves out-of-sample forecasting accuracy and portfolio risk evaluation. Building upon this, a Transformer-based MGARCH model is further proposed, replacing recurrence with self-attention and learnable positional embeddings to better capture long-range dependencies and structural shifts. The Transformer-MGARCH demonstrates superior scalability and robustness, particularly under high-dimensional and volatile market conditions. Overall, this research establishes a hybrid econometric–deep learning paradigm that preserves interpretability while enhancing flexibility and forecasting performance, offering new insights for financial volatility modeling and risk management.