A Discrete-Time Hazard Model for Loans: Some Evidence from Italian Banking System

Abstract

Problem statement: The probability of default, PD, is a crucial problem for banks. In the last years international accords (Basel, Basel 2 and Basel 3) have incentived banks to adopt objectives systems to evaluating and monitoring risk of default in order to predict PD for new loans based on borrower’s characteristics. The aim of this study is to introduce a discrete survival model to study the risk of default and to propose the empirical evidence by the Italian banking system. Approach: Survival analysis is used if we are interested in whether and when an event occurs. In this context the event occurrence represents a borrower’s transition from one state, loan in bonis that is not in default, to another state, the default. In this study through a survival model (in particular a discrete-time hazard model) it is possible verify when the probability of default is the highest considering, for each group of loans, a set of explanatory variables as risk factors of PD. Results: The empirical application obtained through a discrete time hazard model have provided clear evidence that time when the default occurs is an important element to predict the probability of default in time. Regarding Italian data the hazard model shows that explanatory variables (i.e., territorial area, productive economic sector, size of loan and generation of belonging) have effects both on if and on when loan bankrupts. Conclusion: The hazard model estimated for a population of loans involve different probability of default considering conjointly the explanatory variables and the time when the default occurs. Considering jointly the time and the risk factors a probability of default has been modelled for two main groups of loans: “Good borrowers” for which the risk of default is the lowest and “bad borrowers” for which this risk is the highest.