用LSTM增强随机波动率模型，提升标普500波动率预测精度
Stochastic Volatility Modelling with LSTM Networks: A Hybrid Approach for S&P 500 Index Volatility Forecasting
- 将随机波动率模型与LSTM结合，融合统计建模与深度学习优势
- 在1998-2024年标普500日度数据上，预测表现优于单一模型
- 适合金融风控与量化投资研究者参考，尤其关注非线性波动建模
准确的波动率预测对银行、投资和风险管理至关重要，因对未来市场走势的预期直接影响当前决策。本文提出一种混合建模框架，将随机波动率（SV）模型与长短期记忆网络（LSTM）相结合。SV模型提升统计精度并捕捉隐含波动率动态，尤其在应对突发事件时表现优异；LSTM则增强模型对金融时间序列中复杂非线性模式的识别能力。使用1998年1月1日至2024年12月31日的标普500日度数据，采用滚动窗口法训练模型并生成一步向前波动率预测。通过统计检验与投资模拟评估混合模型性能，结果表明该方法优于独立的SV与LSTM模型，为波动率建模技术发展提供支持，有助于提升标普500环境下的风险评估与战略投资规划水平。
原文摘要 · Abstract (English)
Accurate volatility forecasting is essential in banking, investment, and risk management, because expectations about future market movements directly influence current decisions. This study proposes a hybrid modelling framework that integrates a Stochastic Volatility model with a Long Short Term Memory neural network. The SV model improves statistical precision and captures latent volatility dynamics, especially in response to unforeseen events, while the LSTM network enhances the model's ability to detect complex nonlinear patterns in financial time series. The forecasting is conducted using daily data from the S and P 500 index, covering the period from January 1 1998 to December 31 2024. A rolling window approach is employed to train the model and generate one step ahead volatility forecasts. The performance of the hybrid SV-LSTM model is evaluated through both statistical testing and investment simulations. The results show that the hybrid approach outperforms both the standalone SV and LSTM models and contributes to the development of volatility modelling techniques, providing a foundation for improving risk assessment and strategic investment planning in the context of the S and P 500.
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