This study investigates volatility clustering in financial markets and evaluates whether GARCH models effectively capture the time-varying nature of market volatility. Using 4,030 daily observations of S&P 500 Index returns from 2010 to 2026, the study examines return dynamics through autocorrelation and partial autocorrelation analysis, squared-return dependence, and the ARCH Lagrange Multiplier test. The results provide strong evidence of volatility clustering and significant ARCH effects, with the ARCH LM test producing an F-statistic of 15.73 and a p-value below 0.001. A GARCH(1,1) model is estimated to characterize conditional volatility. The estimated persistence, α + β = 0.977, indicates that volatility shocks are highly persistent and take considerable time to dissipate. Conditional volatility analysis further identifies recurring periods of elevated market risk. The findings demonstrate the usefulness of GARCH modelling for measuring and forecasting financial-market volatility, with implications for Value-at-Risk, portfolio management, derivatives pricing, and risk-management decisions.

Key Words: Volatility clustering; GARCH(1,1); financial markets; S&P 500; conditional volatility; ARCH effects; volatility persistence; risk management; time-varying volatility