Financial Risk Modeling and Volatility Forecasting Using GARCH-Based Econometric Techniques

Abstract

This paper examines the evolution, applications, and significance of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models in financial risk modeling and volatility forecasting. Financial markets are characterized by volatility clustering, leptokurtosis, structural breaks, and asymmetric responses to market shocks, making traditional constant-variance models inadequate for modern risk analysis. The study discusses the theoretical foundations of ARCH and GARCH models and highlights the transition toward advanced asymmetric variants such as EGARCH, GJR-GARCH, TGARCH, and APARCH, which better capture leverage effects and non-linear volatility dynamics. Furthermore, the review evaluates estimation approaches including Maximum Likelihood Estimation (MLE), Quasi-Maximum Likelihood Estimation (QMLE), Bayesian inference, and heavy-tailed distribution assumptions for improving forecasting accuracy. Diagnostic testing procedures such as the Ljung–Box test, ARCH-LM test, and information criteria are also explored to assess model adequacy and predictive performance. Particular attention is given to the role of GARCH-based frameworks in calculating Value at Risk (VaR) and Expected Shortfall (ES), which are essential tools for regulatory compliance and portfolio risk management under Basel III standards. The paper additionally investigates the integration of GARCH models with machine learning and deep learning techniques, including GRU and LSTM architectures, to enhance forecasting performance in high-frequency trading and cryptocurrency markets. Sector-specific applications in equity, foreign exchange, energy, and digital asset markets demonstrate the flexibility and robustness of GARCH methodologies. Overall, the review emphasizes that GARCH-based econometric techniques remain indispensable for understanding financial market uncertainty and for supporting data-driven investment and risk management decisions in increasingly volatile global markets.