Models for inflated data applied to credit risk analysis

Abstract

In this thesis, we introduce a methodology based on zero-inflated survival data for the purposes of dealing with propensity to default (credit risk) in bank loan portfolios. Our approach enables us to accommodate three different types of borrowers: (i) individual with event at the starting time, i.e., default on a loan at the beginning; (ii) non-susceptible for the event of default, or (iii) susceptible for the event. The information from borrowers in a given portfolio is exploited through the joint modeling of their survival time, with a multinomial logistic link for the three classes. An advantage of our approach is to accommodate zero-inflated times, which is not possible in the standard cure rate model introduced by Berkson & Gage (1952). The new model proposed is called zero-inflated cure rate model. We also extend the promotion cure rate model studied in Yakovlev & Tsodikov (1996) and Chen et al. (1999), by incorporating excess of zeros in the modelling. Despite allowing to relate covariates to the fraction of cure, the current approach does not enable to relate covariates to the fraction of zeros. The new model proposed is called zero-inflated promotion cure rate model. The second part of this thesis aims at proposing a regression version of the inflated mixture model presented by Calabrese (2014) to deal with multimodality in loss given default data. The novel methodology is applied in four retail portfolios of a large Brazilian commercial bank.