A new Mixture model for the estimation of credit card Exposure at Default

• New Mixture model proposed to estimate outstanding balance over loan and at default.
• Outstanding balance is function of spending and repayment amounts, and credit limit.
• Repeated events survival model to predict probability that balance greater than limit.
• Expected balance and limit estimated using panel models with random effects.
• Overall find more accurate predictions than most of those used in practice especially if short term predictions are required.

Using a large portfolio of historical observations on defaulted loans, we estimate Exposure at Default at the level of the obligor by estimating the outstanding balance of an account, not only at the time of default, but at any time over the entire loan period. We theorize that the outstanding balance on a credit card account at any time during the loan is a function of the spending by the borrower and is also subject to the credit limit imposed by the card issuer. The predicted value is modelled as a weighted average of the estimated balance and limit, with weights depending on how likely the borrower is to have a balance greater than the limit. The weights are estimated using a discrete-time repeated events survival model to predict the probability of an account having a balance greater than its limit. The expected balance and expected limit are estimated using two panel models with random effects. We are able to get predictions which, overall, are more accurate for outstanding balance, not only at the time of default, but at any time over the entire default loan period, than any other particular technique in the literature.