Copula-Based Risk Modeling: A Comparative Analysis of MCAViaR and Gaussian Copulas for Global Indices

This study comparatively analyzes two advanced financial risk modeling frameworks: a copula-based Value-at-Risk (VaR) approach and the Multivariate Conditional Autoregressive Value-at-Risk (MCAViaR) model. We assess their effectiveness in capturing risk dynamics across diverse global markets, using daily log returns from January 1, 2010, to December 31, 2024, for TEDPIX, S&P 500, and BIST 100. This research addresses limitations of traditional linear correlation, especially during market stress.The copula methodology involves two stages: fitting ARMA-GARCH models with Student’s t-distributed innovations for marginal distributions, then employing Gaussian, Student’s t, and Clayton copulas to model inter-market dependence, including tail dependence. MCAViaR, conversely, directly estimates conditional quantiles, adapting to evolving market conditions. Empirical validation is performed through rigorous backtesting, including Kupiec, Christoffersen, and Dynamic Quantile (DQ) tests.Results indicate significant differences. While Student’s t and Clayton copulas effectively capture tail dependence (evidenced by degrees of freedom and positive Clayton parameters), all models—both copula-based and MCAViaR—universally failed the stringent DQ tests across all indices and quantiles. This highlights systematic misspecification in capturing dynamic risk. Despite this, MCAViaR showed a more adaptive nature to sudden market shocks and provided visually more responsive VaR estimates than static copula specifications.The study underscores the necessity of robust, tail-sensitive models for accurate risk assessment in cross-border portfolios. Practical recommendations include adopting Student-t or Clayton copulas, integrating regime-switching mechanisms into MCAViaR, and employing multi-horizon stress testing to enhance dynamic risk management and account for market-specific behaviors.