Back-testing credit risk parameters on low default portfolios: a simple Bayesian transfer learning approach with an application to sovereign risk‖

Sergio Caprioli, Raphael Cavallari, Jacopo Foschi and Riccardo Cogo

Quantitative Finance, 2025, vol. 25, issue 3, 491-508

Abstract: The estimation of Probabilities of Default (PD) is particularly challenging in the context of low-default portfolios. For example, Sovereign portfolios often exhibit very few (or even zero) defaults, making frequentist approaches impractical. Motivated by these considerations, we propose a model based on a simple Bayesian transfer learning approach depending on Expected Default Frequencies (EDF) and observed defaults. The model is founded on a sound statistical methodology, ensuring meaningful risk differentiation and accurate, consistent estimates, with PDs that are strictly monotonic as creditworthiness decreases. In a simulation analysis, we compared the results of this approach with those obtained using transfer learning implemented through a machine learning algorithm. The advantage of the Bayesian model lies in its ease of implementation and interpretation, as well as its ability to ‘automatically’ balance the relevance attributed to observed defaults and the Expected Default Frequencies used as a proxy, without the risk of overfitting.

Date: 2025
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DOI: 10.1080/14697688.2025.2466740

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