Understanding and forecasting equity market volatility has become an essential focus for financial analysts, policymakers, and academic researchers. In this working paper are explained the predictive capabilities of non-linear models—ARCH, GARCH, and EGARCH—using weekly return data from Japan, the UK, and the USA. Covering a 20-year span, their analysis evaluates the performance of these models using standard symmetric loss functions such as ME, RMSE, MAE, and MAPE. The study identifies the EGARCH model as the most reliable tool for capturing the nuances of market volatility, outperforming its counterparts. By exploring the implications of volatility clustering and fat tails in financial time series, this research provides critical insights for derivative traders, portfolio managers, and risk analysts aiming to improve market predictions and enhance risk management strategies. This article highlights the methodologies, empirical findings, and broader implications of their innovative approach to volatility modelling.