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 small and medium-sized enterprises (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. The resulting problem is a mixed-integer nonlinear program, which is NP-hard. In this paper, we propose an approximate optimization problem that combines a large pool approximation, linearization of ancillary variables, and clustering. This approximate optimization problem delivers a solution (i) that improves the value of the objective function under the exact criterion compared to the solution of a derivative-free mixed-integer algorithm solving the exact problem and (ii) in a much lower computation time. As illustration, we consider two realistic CLO 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.