GARCH-Informed Neural Networks for Volatility Prediction in Financial Markets

TL;DR

The paper tackles volatility forecasting in financial markets, addressing limitations of linear ARCH/GARCH models by introducing a GARCH-Informed Neural Network (GINN), a PINN-inspired hybrid that blends GARCH dynamics with LSTM-based calibration. The method uses a two-phase architecture and a tunable loss weight $\lambda$ to combine ground-truth volatility with GARCH predictions, with a variant GINN-0 that relies solely on GARCH supervision. Across seven global indices and multiple baselines, GINN and GINN-0 deliver superior out-of-sample performance in terms of $R^2$, $\text{MSE}$, and $\text{MAE}$, while producing smoother volatility trajectories that better capture short-term features. The results suggest a robust, generalizable framework for physics-informed hybrid time-series forecasting in finance, with potential benefits for risk management and derivative pricing; future work includes exploring alternative ARCH extensions and more nuanced performance metrics.

Abstract

Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its succeeding variants are well established models for stock volatility forecasting. More recently, deep learning models have gained popularity in volatility prediction as they demonstrated promising accuracy in certain time series prediction tasks. Inspired by Physics-Informed Neural Networks (PINN), we constructed a new, hybrid Deep Learning model that combines the strengths of GARCH with the flexibility of a Long Short-Term Memory (LSTM) Deep Neural Network (DNN), thus capturing and forecasting market volatility more accurately than either class of models are capable of on their own. We refer to this novel model as a GARCH-Informed Neural Network (GINN). When compared to other time series models, GINN showed superior out-of-sample prediction performance in terms of the Coefficient of Determination ($R^2$), Mean Squared Error (MSE), and Mean Absolute Error (MAE).

Figures (8)

• Figure 1: The variance prediction workflow diagram for GARCH-type models
• Figure 1: Performance Results of Models in the Out-of-Sample Testing Dataset
• Figure 2: The variance prediction workflow diagram for the LSTM model
• Figure 3: The model structure of the LSTM model
• Figure 4: The variance prediction workflow diagram for the GINN model