Definition of Bad in Probability of Default model

[Ujjawal]

I'm in the process of building a PD model for credit card product. I am confused in creating a dependent variable. A customer who has experienced delinquency 90 or more days considered 'bad' customer otherwise good. Let's take following scenarios -
1. He has not paid 2 times - 1 to 29 and 30 to 59 days but paid a single time minimum payment in the third stage 60 to 89 days. Is he considered as 'bad'?

2. He has made multiple trans actions in the 2nd and 3rd month so his overdue amount is increased. If he pays minimum payment of the total unpaid amount in the third month, Would he be considered as a' bad ' customer?

[SASKiwi · Accepted solution]

I'm assuming here that you are building a PD model for the purpose of doing Basel II/III type credit risk calculations.

As a general rule with credit card systems if you make the minimum payments on time regardless of any other transactions then you are not in arrears. Also if you make a payment usually the oldest debt is reduced first.

I suggest that in both of the cases you mention, if the customer has paid at least the minimum payment due from month 1, in month 3 they will not be in default as the oldest debt is paid off first. If their payment does not clear the month 1 minimum payment then they will be in default as there is some remaining debt that is 90 days old. Here I'm defining a month as 30 days.

You may also need to consider what happens with overlimit cards. Usually most card systems allow small overlimits to happen but eventually you are required to pay this back and you may be required to pay more than the minimum to get the card back under limit.

If you are working on a Basel-type PD model, your definition of default should also include "serious" card blocks like card in Collections, Bankrupt, Credit Counselling, Paying off by installment. These are system-dependent so I can only guide you of what to look for.

All these definitions should be reviewed and confirmed with the help of card system and business experts and these are highly system dependent.  

[Ujjawal]

Thank you so much for your detailed explanation. I really appreciate it.  One last question -  If a customer holds multiple credit cards, should i include information of both the accounts. Is PD model built at account level or customer level? How both the card information should be used in the model?

[JasonXin]

Ujjawal

First, thanks  for using SAS. My name is Jason Xin, analytics solution architect focused on financial services.

Regarding account level vs. individual level given some have >1 CC acccount, you should model on individual level, aggregating all the input variables across all CC accounts under individuals. You could consider building a flag to indicate single account or multiple accounts for testing (significance test, story telling, profiling, insights, model lift...). As long as you don't create/engage (too many) new variables just to measure either single or multiple groups. You should have good control over creating new variables. Engaging existing data could be intriguing. If your models involve external account data on the bureau side, you may not have 'equal' access to all the data over all the multiple accounts all the time. Sometimes they are OK at model building time, but not sustainable at scoring. So a bit planning ahead is more important than technical jogging.

Whether you build one model for all, or build one for single account and another for multiple accounts, eventually you need to aggregate individual models to one for the individual to support decisions; piecing together segment based models can be tricky as well. We simply do not say your credit score on Discover  is 820  and  your credit score on Amex card is 740. We say your SSN shows your score is 785.

Hope this helps. Thanks for using SAS. Happy holiday.

Best Regards

Jason Xin