Estimating a discrete distribution subject to random left-truncation with an application to structured finance

Risk-based pricing within consumer lending is ubiquitous. It considers both prevailing interest rates and the credit profile of a borrower to determine the cost of borrowing. All else equal, higher default risks pay higher borrowing costs. This cost is the annual percentage rate (APR), and it is set at the loan’s origination. A borrower’s credit profile is dynamic, however, and the risk of default gradually declines for current loans. In this article, we derive a novel large-sample statistical hypothesis test suitable for loans sampled from asset-backed securities to populate a credit risk transition matrix between consumer credit risk groups. We find that current loans in all risk groups eventually converge to the top credit tier before scheduled termination, a phenomenon we call credit risk convergence. We then use these convergence estimates for two empirical economic studies. We first estimate that lender conditional risk-adjusted expected profits significantly increase as high-risk, high-APR borrowers stay active and paying. We then estimate current borrowers are entitled to $1,153–2,327 in potential credit-based savings from their improving risk profiles. Because we study consumer auto loans, a large-scale and essential economic good, we opine on the social implications of these results and suggest areas of further study.

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Estimating a discrete distribution subject to random left-truncation with an application to structured finance

Cited by 2 publications

References 35 publications

On the maximum likelihood estimation of a discrete, finite support distribution under left-truncation and competing risks

On the maximum likelihood estimation of a discrete, finite support distribution under left-truncation and competing risks

On the convergence of credit risk in current consumer automobile loans

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