🤖 AI Summary
Addressing the challenge of simultaneously achieving structural interpretability and data adaptability in S&P 500 volatility forecasting, this paper proposes the SV-LSTM hybrid model—the first end-to-end jointly trained framework integrating stochastic volatility (SV) latent-variable modeling with long short-term memory (LSTM) networks. The model synergistically combines the statistical rigor of SV models with LSTM’s capacity to capture nonlinear temporal dynamics, enhanced by rolling-window training and Monte Carlo likelihood estimation for robustness. Empirical evaluation over 1998–2024 demonstrates that SV-LSTM reduces mean squared error (MSE) by 23.7% relative to standalone SV or LSTM baselines and achieves a 96.4% pass rate in Value-at-Risk (VaR) backtesting. These results indicate substantially improved stability in extreme-event volatility forecasting, offering a theoretically grounded and empirically effective tool for risk management and dynamic asset allocation.
📝 Abstract
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.