In this paper, we use a copula to examine the relationship and dynamic dependence structure between the crude oil market and the BRICS countries’ stock indices expressed through financial crises, from the 2008 global financial crisis to COVID-19, based on daily data. We characterize the long-term relationship as well as the short-term dynamics and represent the interdependence between them. We also study the short-run conditional links through the considered variables under the effects of long-run interactions and the asymmetric volatility spillover relationship. In addition, we establish that the volatility transmission is stubborn and that the impact of the crises and our empirical findings prove that there is fractional co-integration between crude oil and financial markets. We notice that there are lengthy correlations between the variables, as we detect significant bidirectional causal links. In particular, we see positive short-run links and use an optimal copula coefficient to measure the risk spillovers between oil markets and financial markets that represent the dependence structure. For robustness purposes, based on a sliding-window analysis, we complement our investigation with VaR analysis.