Estimating the risk of joint defaults: an application to central bank collateralized lending operations

Central bank lending to commercial banks is typically collateralized which reduces central bank’s credit risk exposure to “double default events” when the counterparty and the issuer of the underlying collateral asset both default in a short period of time. This paper presents a simple model for correlated defaults which are the key drivers of residual credit risk in central bank’s repo portfolios. In the model default times of counterparties and collateral issuers are determined by idiosyncratic and systematic factors, whereby a name defaults if it is struck by either factor for the first time. The novelty of our approach lies in representing systematic factors as increasing sequences of random variables. Such a setting allows to build a rich dependence structure that is free of the flaws inherent in the Gaussian copula-based approaches currently regarded as state of the art solutions for central banks.