用深度学习改进金融波动率模型，提升风险预测能力
Deep Learning Enhanced Multivariate GARCH
- 将LSTM引入BEKK模型，捕捉金融收益的非线性动态依赖
- 在多个股市数据上显著优于传统模型的风险预测表现
- 兼顾深度学习强拟合与经济模型可解释性，适合量化风控场景
本文提出一种新型多变量波动率建模框架——长短期记忆增强型BEKK（LSTM-BEKK），将深度学习融入多变量GARCH过程。通过结合循环神经网络的灵活性与BEKK模型的计量经济学结构，该方法能更好捕捉金融收益数据中的非线性、动态及高维依赖关系。模型克服了传统多变量GARCH方法在持续波动聚集和资产间非对称联动方面的局限，利用LSTM的数据驱动特性，有效适应时变市场环境，提升鲁棒性与预测性能。实证结果表明，LSTM-BEKK在多个股票市场中均实现了更优的样本外投资组合风险预测表现，同时保持了BEKK模型的可解释性。这些发现凸显了混合计量-深度学习模型在金融风险管理与多变量波动率预测中的潜力。
原文摘要 · Abstract (English)
This paper introduces a novel multivariate volatility modeling framework, named Long Short-Term Memory enhanced BEKK (LSTM-BEKK), that integrates deep learning into multivariate GARCH processes. By combining the flexibility of recurrent neural networks with the econometric structure of BEKK models, our approach is designed to better capture nonlinear, dynamic, and high-dimensional dependence structures in financial return data. The proposed model addresses key limitations of traditional multivariate GARCH-based methods, particularly in capturing persistent volatility clustering and asymmetric co-movement across assets. Leveraging the data-driven nature of LSTMs, the framework adapts effectively to time-varying market conditions, offering improved robustness and forecasting performance. Empirical results across multiple equity markets confirm that the LSTM-BEKK model achieves superior performance in terms of out-of-sample portfolio risk forecast, while maintaining the interpretability from the BEKK models. These findings highlight the potential of hybrid econometric-deep learning models in advancing financial risk management and multivariate volatility forecasting.
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