We study the effect of dealer exit on prices and quantities in a model of an over-the-counter market featuring a core-periphery network with bilateral trading costs. The model is calibrated using regulatory data on the entire U.S. credit default swap (CDS) market between 2010 and 2013. Prices depend crucially on the risk-bearing capacity of core dealers, yet unlike standard models featuring a dealer sector, we allow for heterogeneity in dealer risk-bearing capacity. This heterogeneity is quantitatively important. Depending on how well dealers share risk, the exit of a single dealer can cause credit spreads to rise by 8 % to 24%.