On loss distributions from installment-repaid loans

The banks have been accumulating huge data bases for many years and are increasingly turning to statistics to provide insight into customer behaviour, among other things. Credit risk is an important issue and certain stochastic models have been developed in recent years to describe and predict loan default. Two of the major models currently used in the industry are considered here, and various ways of extending their application to the case where a loan is repaid in installments are explored. The aspect of interest is the probability distribution of the total loss due to repayment default at some time. Thus, the loss distribution is determined by the distribution of times to default, here regarded as a discrete-time survival distribution. In particular, the probabilities of large losses are to be assessed for insurance purposes.