This study examines the volatility dynamics of eight major stock market indices using a comprehensive set of parametric and semiparametric generalized autoregressive conditional heteroskedasticity (GARCH) models, including long-memory variants such as fractionally integrated GARCH (FIGARCH) and fractionally integrated log-GARCH (FI-Log-GARCH). The research utilizes daily closing values from January 2004 to April 2025 to identify the most effective models for forecasting value at risk (VaR) and expected shortfall (ES) by evaluating their performance through backtesting methods, including traffic light tests and the weighted average distance (WAD) selection criterion. The findings reveal that semiparametric models, particularly Semi-FIGARCH, outperform traditional parametric models in capturing asymmetric effects and long-memory properties in financial time series data. These models provide more accurate and robust volatility forecasts, especially during periods of market turbulence. The study underscores the importance of incorporating advanced volatility models into risk management frameworks to enhance financial stability and decision-making in global markets. The insights derived from this research offer practical implications for investors, risk managers and regulators, emphasizing the need for adaptable and comprehensive volatility modelling techniques in financial markets.
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