Regime-Dependent Dynamics Between the S&P 500 and VIX: A Multi-Method Analysis of Nonlinear Dependence, Tail Risk, and Post-COVID Market Structure (2020–2024)

This study investigates the dynamic, nonlinear, and regime-dependent relationship between the S&P 500 and the CBOE Volatility Index (VIX) over the period January 2020–December 2024, a timeframe characterized by unprecedented market stress and post-crisis normalization. Using a unified empirical framework that integrates Markov-Switching VAR, DCC-GARCH volatility modeling, and Student-t copula–EVT tail dependence estimation, the analysis reveals strong asymmetric and time-varying interdependence between equity returns and implied volatility. The results show that return distributions of the S&P 500 become significantly more hazardous in high-VIX regimes, exhibiting elevated volatility, negative skewness, and substantial excess kurtosis. Dynamic correlations fluctuate between − 0.25 and − 0.89, intensifying sharply during crisis periods. The lower-tail dependence coefficient (λ_L = 0.41) confirms the heightened probability of simultaneous large equity losses and VIX spikes, while upper-tail dependence remains negligible. Furthermore, post-2022 markets exhibit a persistent shift toward a structurally higher volatility baseline compared with pre-COVID norms. These findings provide new evidence on regime-dependent risk transmission and offer practical implications for tail-risk hedging, portfolio allocation, and volatility-sensitive strategies.