Central counterparties (CCPs) have increasingly become a cornerstone of financial markets infrastructure. We present a model where trades are time-critical, liquidity is limited and there is limited enforcement of trades. We show a CCP novating trades implements efficient trading behaviour. It is optimal for the CCP to face default losses to achieve the efficient level of trade. To cover these losses, the CCP optimally uses margin calls, and, as the default problem becomes more severe, also requires default funds and then imposes position limits.