Analysis of defaulters' behaviour using the Poisson-mixture approach
Department of Statistics, Athens University of Economics, 76 Patission Street, Athens, 10434 Greece
Institut Superieur de Gestion de Tunis et UAQUAP, 41 Rue de la Liberte, Bouchoucha, le Bardo 2000, Tunisia
Email: karlis{at}aueb.gr
Email: mohieddine.rahmouni{at}isg.rnu.tn
Received on 20 February 2006. Accepted on 25 April 2007.
Credit scoring is of major interest to financial institutions as a mean of controlling their capital allocation and increasing their profitability. Classical credit-scoring approaches are based on a ‘good’ or ‘bad’ basis, i.e. by classifying new applicants into one of the two possible categories based on a series of their characteristics. This strongly depends on the definition of good and bad customers. We adopt a different approach. Instead of trying to predict the class of a new applicant, we try to predict the number of defaults in the near future. Previous attempts toward this idea have used negative binomial regression models to fit the data. We fit finite Poisson mixtures treating the number of components unknown which have to be estimated from the data. Using covariates in all components, we reveal the impact of several demographic variates in creating the different groups of customers but we are able to predict for each customer the group to which he belongs, as well his expected number of defaults. This is of particular interest for financial purposes as it allows the estimation of the expected loss from each customer and thus the ability to create rules for providing the loan on a personal basis. This classification allows the means to determine the optimal interest rate to maximize bank profit under asymmetrical information. This paper uses real data and compares various models focusing on the finite Poisson mixture regression models.
Keywords: credit scoring; personal loans; count data; finite Poisson mixture model; optimal interest rate; asymmetrical information