One-factor model for default rates by loan type

Abstract

This paper investigates the link between default rates by loan types and the systemic credit risk component. This link is described by a linear model that combines systemic and idiosyncratic contributions. The systemic component is a latent factor that depends directly on the aggregate loan default rate, while the idiosyncratic component drives specific variations of default rates across loan types. By transforming observable risk measures, the model can be econometrically represented as a mixed-effects model, where the systemic and idiosyncratic components represent, respectively, the slope and the intercept that are specific for each loan type individually. The proposed model is illustrated on a panel of defaulted loans of the Association of Serbian Banks. The obtained results show the model's very high power in explaining average default rates for all loan types. Thus, the aggregate default rate plays the role of a unique systemic component that mimics the influence of fundamental macroeconomic risk factors easily, without the necessity to model this relationship explicitly.

Keywords

• credit risk
• default rate
• systemic factors
• mixed-effects model