Default prediction of SMEs by a generalized extreme value additive model

A new model is proposed for default prediction of Small and Medium Enterprises (SMEs). The main weakness of the scoring models proposed in the literature is not to consider the default as a rare event. To take into account this characteristic, Calabrese and Osmetti (2011) suggested the quantile function of the Generalized Extreme Value (GEV) distribution as a link function in a Generalized Linear Model (GLMs). In the GLMs, the relationship between the independent variable and the predictor is constrained to be linear. Since this assumption is not usually satisfied by scoring models, a Generalized Additive Model (GAM) is suggested with the quantile function of the GEV distribution as link function. Hence, the Generalized Extreme Value Additive (GEVA) model is proposed. Finally, our proposal is applied to empirical data on Italian SMEs. It is obtained that the GEVA model shows a high accuracy for predicting defaults.