Modelling credit risk with scarce default data: on the suitability of cooperative bootstrapped strategies for small low-default portfolios

Credit risk models are commonly based on large internal data sets to produce reliable estimates of the probability of default (PD) that should be validated with time. However, in the real world, a substantial portion of the exposures is included in low-default portfolios (LDPs) in which the number of defaulted loans is usually much lower than the number of non-default observations. Modelling of these imbalanced data sets is particularly problematic with small portfolios in which the absence of information increases the specification error. Sovereigns, banks, or specialised retail exposures are recent examples of post-crisis portfolios with insufficient data for PD estimates, which require specific tools for risk quantification and validation. This paper explores the suitability of cooperative strategies for managing such scarce LDPs. In addition to the use of statistical and machine-learning classifiers, this paper explores the suitability of cooperative models and bootstrapping strategies for default prediction and multi-grade PD setting using two real-world credit consumer data sets. The performance is assessed in terms of out-of-sample and out-of-time discriminatory power, PD calibration, and stability. The results indicate that combinational approaches based on correlation-adjusted strategies are promising techniques for managing sparse LDPs and providing accurate and well-calibrated credit risk estimates.