A comparative analysis of the UK and Italian small businesses using Generalised Extreme Value models

This paper presents a cross-country comparison of significant predictors of small business failure between Italy and the UK. Financial measures of profitability, leverage, coverage, liquidity, scale and non-financial information are explored, some commonalities and differences are highlighted. Several models are considered, starting with the logistic regression which is a standard approach in credit risk modelling. Some important improvements are investigated. Generalised Extreme Value (GEV) regression is applied in contrast to the logistic regression in order to produce more conservative estimates of default probability. The assumption of non-linearity is relaxed through application of BGEVA, non-parametric additive model based on the GEV link function. Two methods of handling missing values are compared: multiple imputation and Weights of Evidence (WoE) transformation. The results suggest that the best predictive performance is obtained by BGEVA, thus implying the necessity of taking into account the low volume of defaults and non-linear patterns when modelling SME performance. WoE for the majority of models considered show better prediction as compared to multiple imputation, suggesting that missing values could be informative

UNCERTAINTY INTERVAL TO ASSESS PERFORMANCES OF CREDIT RISK MODELS

reserved2In this paper, we propose a novel approach to compare the performances of binary classification models with an application on a real data set on credit risk provided by Unicredit bank. Starting from the probability of default estimated by each predictive model under comparison, the idea is to derive an uncertainty interval comparing the predictions with the observed target variable. A model is considered to have good performances if the associated uncertainty interval is small. The shape of the uncertainty interval provides also some information about the model performances in terms of classification errors, false positive and false negative. The uncertainty interval permits to compare different models without selecting a binarization threshold and it applies both for parametric and non parametric predictive models.mixedSilvia Figini; Pierpaolo UbertiFigini, Silvia; Uberti, Pierpaol