Using copula methods and simulation-based inference the authors address the association between the performance of the stocks of European banks and the CDS markets. Their analysis has three purposes: (i) analysing the dependence structure of the markets when extreme events occur; (ii) checking the validity of the conclusion of Merton (On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, 1974) and other similar structural models concerning the intensification of the relationship between stock prices and credit spreads during financial distress periods; (iii) analysing the auto-covariance of the dependence structure. First, the results show symmetric dependence and tail dependency equality between the two markets. This means that, surprisingly, the association between stock prices and spreads of the banking sector does not seem to surge in financial distress periods, contradicting the conclusions of Merton (1974) and other structural models, which could be related with a “too-big-to-fail” effect. Second, the authors do not detect structural breaks in the dependence structure in a period marked by the U.S. financial crisis (2008) and the European sovereign debt crisis (2010), which posed concerns on the European financial system health. Finally, they find evidence that the dependence between the markets is autoregressive and possibly time variant. The authors suggest that the inexistence of a higher negative tail dependence between the filtered returns may reside in the “too-big-to fail” effect, that is, credit holders receive a subsidy from governments protecting them from bankruptcy costs, contrary to what happens with equity holders whose capital is wiped-out if the bank fails.