Stochastic Volatility Modelling with LSTM Networks: A Hybrid Approach for S&P 500 Index Volatility Forecasting

TL;DR

This paper introduces a hybrid model combining stochastic volatility and LSTM neural networks to improve the accuracy of S&P 500 index volatility forecasts, aiding better risk management and investment decisions.

Contribution

It presents a novel hybrid framework that integrates SV models with LSTM networks, enhancing volatility prediction by capturing latent dynamics and nonlinear patterns.

Findings

Hybrid model outperforms standalone SV and LSTM models.

Improves volatility forecasting accuracy for S&P 500.

Supports better risk assessment and investment strategies.

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.