Jointly Modeling Dynamic Dependence and Volatility in Natural Resource and Energy Indices Using a Multivariate t-Copula eGARCH Model

Abstract

This study develops a robust framework for modeling dynamic volatility, asymmetry, and tail dependence in financial returns, focusing on the daily returns of Natural Resource Index (NRI) and the Oil and Gas Index (OGI). Standard multivariate volatility models, such as DCC-GARCH, often fail to adequately capture extreme co-movements, asymmetric dependence, and tail risk under non-normality, potentially producing biased variance and correlation estimates. To address these limitations, we propose a copula-based eGARCH model with multivariate Student-t (MVT) marginals, which jointly captures log-volatility dynamics and flexible tail dependence. Among 18 candidate models, the Copula-eGARCH-MVT model with eGARCH marginals and a multivariate Student-t copula provided the best fit, effectively accounting for heavy tails, volatility clustering, asymmetry, and dynamic dependence. Monte-Carlo simulations based on the empirical estimation confirmed that this framework reduces variance estimation bias, improves coverage probabilities, and more accurately models dynamic correlations and tail risk compared to standard DCC-GARCH models. This Monte-Carlo study showed that the coverage probability achieved by the eGARCH model is closer to the target 95% due to eGARCH’s ability to capture asymmetric volatility and heavy-tailed behavior in financial returns. Overall, the proposed Copula–eGARCH–MVT framework offers superior performance and risk assessment, providing a comprehensive tool for portfolio management, Value-at-Risk estimation, and the analysis of complex dependence structures in financial markets exhibiting asymmetric shocks and heavy-tailed behavior.