GARCHNet: Value-at-Risk Forecasting with GARCH Models Based on Neural Networks

Area of Science:

• Econometrics
• Computational Finance
• Machine Learning

Background:

• Classical Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are widely used in financial modeling, particularly for Value-at-Risk (VaR) calculations, due to their effectiveness in capturing volatility.
• However, traditional GARCH models often lack the necessary nonlinear structure to accurately represent conditional variance.
• The advancement of deep learning methods offers powerful tools for modeling intricate nonlinear relationships in financial data.

Purpose of the Study:

• To propose a novel nonlinear approach, GARCHNet, for modeling conditional variance by integrating Long-Term Short-Term Memory (LSTM) neural networks with GARCH.
• To address the limitations of classical GARCH models in capturing nonlinear dynamics in financial markets.
• To evaluate the performance of GARCHNet across various financial indices and volatility regimes.

Main Methods:

• Development of GARCHNet, a hybrid model combining LSTM architecture with maximum likelihood estimation within the GARCH framework.
• Application of GARCHNet to model conditional variance using normal, t, and skewed t distributions.
• Empirical analysis using logarithmic returns from WIG 20, S&P 500, and FTSE 100 indices over multiple time periods (2005-2021).

Main Results:

• The GARCHNet model demonstrates the ability to effectively capture nonlinear structures in conditional variance, outperforming traditional models in certain aspects.
• Empirical results on major stock indices confirm the validity and potential of the proposed GARCHNet approach.
• The study highlights the adaptability of the model to different variance distributions and its robustness across varying market volatility.

Conclusions:

• GARCHNet offers a promising nonlinear extension to GARCH modeling, enhancing the representation of conditional variance in financial time series.
• The integration of LSTM networks provides a powerful mechanism for capturing complex dependencies missed by linear GARCH specifications.
• Further research can explore extensions to other distributions and advanced LSTM architectures for even greater accuracy in financial volatility forecasting.