Credit selection in Collateralized Loan Obligation: efficient approximation through linearization and clustering

Despite its role in the global financial crisis, collateralized loan obligation (CLO) remains a powerful tool to direct funds towards the real economy. In particular, it enables development banks to increase credit supply to SMEs. Public financial institutions thus face the challenge of identifying a subset of credits to be pooled in a CLO for the sake of reaching a specific financial target. This is a mixed-integer nonlinear program, known to be NP-hard. In this paper, we provide an efficient method to tackle this problem by relying on the large pool approximation combined with clustering and linearization of ancillary variables. As illustration, we consider two objective functions. We rely on the celebrated one-factor Gaussian copula in the main examples, but make clear that this assumption is not a restriction and can be relaxed. Our results contribute to reduce the funding cost of SMEs and are of direct interest for securitization stakeholders such as public financial institutions, commercial banks and pension funds.