The interconnectedness of financial institutions affects instability andcredit crises. To quantify systemic risk we introduce here the PD model,a dynamic model that combines credit risk techniques with a contagionmechanism on the network of exposures among banks. A potential lossdistribution is obtained through a multi-period Monte Carlo simulationthat considers the probability of default (PD) of the banks and theirtendency of defaulting in the same time interval. A contagion processincreases the PD of banks exposed toward distressed counterparties. Thesystemic risk is measured by statistics of the loss distribution, whilethe contribution of each node is quantified by the new measures PDRankand PDImpact. We illustrate how the model works on the network of theEuropean Global Systemically Important Banks. For a certain range of thebanks' capital and of their assets volatility, our results reveal theemergence of a strong contagion regime where lower default correlationbetween banks corresponds to higher losses. This is the opposite of thediversification benefits postulated by standard credit risk models usedby banks and regulators who could therefore underestimate the capitalneeded to overcome a period of crisis, thereby contributing to thefinancial system instability.