Assessing Volatility Models for the S&P 500: A focus on traditional models and volatility cycle influence

Abstract

This study evaluates traditional volatility models in forecasting and fitting S&P 500 Realised Volatility over the past 30 years. The first objective, based on Main Group 1, analyzes post2017 forecasts and in-sample fit over the previous decades. Box Jenkins models such as ARMA, ARFIMA, and AR showed strong performance, with 𝑅" above 90 % and MAPE near to 15 %. Their rankings for fit and forecast were closely aligned, a rare result in the literature, and remained consistent across different metrics despite a clear tendency to underestimate volatility. The second objective uses Main Group 2 to examine model performance across volatility regimes. Unlike the first phase, this part revealed a disconnect between fit and forecasting accuracy. Still, the top models remained competitive across regimes, with declining accuracy performance under rising volatility but improved directional outcomes in highly volatile phases. Comparing both groups shows that dataset size affects model behaviour differently depending on whether value or direction is prioritized. Overall, the results question the dominance of ARCH and stochastic volatility models, showing that simpler Box Jenkins models, when well calibrated, offer robust and practical forecasts. The findings support a portfolio approach, matching models to specific forecasting goals since no single model consistently outperformed across all metrics.