The authors propose a general framework for estimating the likelihood of default by central counterparties (CCP) in derivatives markets. Unlike conventional stress testing approaches, which estimate the ability of a CCP to withstand nonpayment by its two largest counterparties, the authors study the direct and indirect effects of nonpayment by members and/or their clients through the full network of exposures. They illustrate the approach for the credit default swaps (CDS) market under shocks that are similar in magnitude to the Federal Reserve’s 2015 Comprehensive Capital Analysis and Review trading book shock. The analysis indicates that conventional stress testing approaches may underestimate the potential vulnerability of the main CCP for this market.