Low Default Portfolios—A Proposed Rule to Identify Differences between Imprudence, Conservatism, and Exaggeration

Abstract

Internal models may be used by banks to calculate their regulatory capital for credit risk. There are a variety of methodologies for estimating default probabilities, which leads to major differences in credit provisions and capital requirements. Using either a classical or a Bayesian technique, the computation of default probabilities can be ensured. Reduced form models are a choice. These models, however, might not be used to quantify economic capital because they assume independence among default events. Banks are compelled to employ structural models since defaults in the real world of banking are not solely due to exogenous causes. Because of the diversification effects between credit losses for one obligor and credit losses for other obligors in each bank’s portfolio, total unexpected losses do not equal the sum of individual unexpected losses. Those two types of models—reduced form and structural—are provided in either a theoretical or a numerical format. This paper covers both the classical and Bayesian techniques, with the latter employing a broader set of prior functions that offer considerably different probabilities. Distinguishing between imprudence, conservatism, and exaggeration might be difficult in the context of low default portfolios with scarce data. A realistic rule is proposed for finding the minimum and maximum bounds and therefore assessing the required conservatism margin by comparing classical and Bayesian probabilities.