Nonparametric estimation of the probability of default in credit risk

Abstract

Financial institutions are interested in knowing the probability that their clients declare themselves unable to pay the debts incurred by granting a credit. The aim of this work is to propose models to estimate this probability, called probability of default (PD), using the information provided by the credit scoring. The PD conditional on the credit scoring can be written as a transformation of the conditional survival function of the variable “time to default”. This property is used to propose new PD estimators, based on nonparametric estimators of the survival function. The time to default faces a right-censoring problem, since in the study of a set of loans, it is not possible to observe default for all of them. Consequently, censored data techniques and survival analysis are used. Given the possible existence of individuals not susceptible to default, mixture cure models are also discussed in this work. The asymptotic expression for the mean squared error and the asymptotic normality of the proposed estimators are obtained. Automatic bootstrap selectors are proposed for the smoothing parameters on which the estimators depend. The performance of the proposed techniques is analysed and compared with existing semiparametric approaches through simulation studies and illustrated by analysing bank loan data