Long-Term Volatility Dynamics Of The German Stock Market: Insights From Two Decades Of Daily Returns

This study provides an empirical analysis of the volatility dynamics of the Deutscher Aktienindex (DAX) stock index over a 20-year period based on daily observations, specifically from January 2, 2006, to March 20, 2026. Utilizing a dataset of 5,140 daily return points, the research explores the time-varying nature of market risk and the presence of volatility clustering. The primary objective is to identify a robust econometric framework capable of capturing the asymmetric response of volatility to market shocks, commonly known as the leverage effect. To achieve this, the study evaluates several GARCH-family models specifications, including GARCH, EGARCH, GJRGARCH, and APARCH models, paired with various error distributions such as Normal, Student-t, GED, and Skewed-t. Initial testing confirms that the return series is stationary, non-normally distributed, and characterized by significant "fat tails". Based on the lowest Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), the GJR-GARCH model with a Skewed-t distribution is identified as the most suitable model for the DAX index. The results demonstrate high volatility persistence and provide strong evidence of the leverage effect, where negative market shocks impact volatility more significantly than positive ones. Diagnostic checks, including the Ljung-Box test, confirm that the model successfully captures the underlying volatility structure. These findings offer valuable insights for investors and policymakers regarding risk assessment and strategic decision-making in the German equity market.