<![CDATA[This study investigates the comparative performance of symmetric and asymmetric GARCH-family models in capturing volatility dynamics and forecasting stock market volatility, using S&P 500 index data spanning 2023–2025. The primary objective is to evaluate whether asymmetric models that account for leverage effects whereby negative shocks exert disproportionately larger impacts on volatility than positive shocks of comparable magnitude offer superior in-sample fit and out-of-sample predictive accuracy relative to symmetric specifications. Methodologically, daily closing prices are transformed into logarithmic returns, with the conditional mean modeled using ARIMA and the conditional variance estimated through GARCH, GJR-GARCH, and EGARCH specifications. Model selection is based on the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), while out-of-sample forecasting performance is assessed using MSE, RMSE, MAPE, and R² measures. Empirical results reveal that asymmetric models, particularly GJR-GARCH, achieve superior in-sample performance according to information criteria, reflecting the presence of leverage effects in stock market volatility. However, the standard GARCH model delivers more consistent and accurate out-of-sample volatility forecasts. This finding highlights a critical distinction: models achieving the lowest AIC or BIC values do not necessarily provide the most accurate volatility predictions, particularly over extended forecasting horizons. From a practical standpoint, these results carry important implications for risk managers and portfolio analysts. When the primary objective is volatility prediction for hedging or risk assessment purposes, simpler symmetric models may be preferable due to their forecasting stability. Conversely, asymmetric models remain valuable for understanding market dynamics and the differential impact of positive versus negative shocks on volatility behavior.]]>
