Modelling credit risk in portfolios of consumer loans: transition matrix model for consumer credit ratings

The corporate credit risk literature has many studies modelling the change in the credit risk of corporate bonds over time. There is far less analysis of the credit risk for portfolios of consumer loans. However behavioural scores, which are commonly calculated on a monthly basis by most consumer lenders are the analogues of ratings in corporate credit risk. Motivated by studies in corporate credit risk, we develop a Markov chain model based on behavioural scores to establish the credit risk of portfolios of consumer loans. We motivate the different aspects of the model – the need for a second order Markov chain, the inclusion of economic variables and the age of the loan – using data on a credit card portfolio from a major UK bank