This paper introduces an incentive compatibility framework to analyze agency problems linked to central counterparty (CCP) risk management. Our framework, which is based on a modern approach to extreme value theory, is used to design CCP skin-in-the-game (SITG). We show that under inadequate SITG levels, members are more exposed to default losses than CCPs. The resulting risk management incentive distortions could be mitigated by using the proposed SITG formulations. Our analysis addresses investor-owned and member-owned CCPs, we also analyze multilayered and monolayer default waterfalls. Viewing the total size of SITG as the lower bound on CCP regulatory capital, the framework can be used to improve capital regulation of investor-owned and member-owned CCPs. We also demonstrate that bank capital rules for CCP exposures may underestimate risk. The broader central clearing mandate of U.S. Treasuries may take place under monolayer CCPs. These clearinghouses may need to allocate more of their own capital to the default waterfall.