The definition of default is one of those things that sounds easy at a high level, but can get fuzzy when you get down to the details - like writing a computer program to build the default information.

Representing the high level we have Basel[452] quoted in part: “… The obligor is past due more than 90 days on any material credit obligation … Overdrafts will be considered as being past due once the customer has breached an advised limit…”

So default has a time dimension as well as an amount dimension. The “amount” is basically dollars but may perhaps be expressed as a percentage (of a dollar limit). Materiality considerations apply to the amount - credit obligations below some threshold are not material and would not trigger Basel-default no matter how long past due.

How should this materiality threshold be chosen? Need it have any relation to the level at which the bank would write off an account as uneconomic to pursue collection activities on? Presumably, no; one would choose a fairly low and stable default materiality for Basel-default purposes of, say, $100, to be as inclusive as possible and avert any argument that true defaults were being buried.

There should be no risk capital cost of having an inclusive default definition because, although it would lead to higher PDs than a definition with a $250 threshold, it should lead to corresponding lower EAD and LGD. (Although this point sounds right in principle, there might be technical objections to it depending on the maths of the formulas and how they work together.)

OTOH, the write-off level for collections is a movable feast depending on many factors - such as product type, collections technology and resources, stages of the collection/recovery process - that could not provide a stable baseline for a definition. Clearly also, the bank would want to recognise that category of defaults that was material enough to be considered a default but not material enough to go through the full collection/recovery processes.

The downside to making a default definition too inclusive - such that it flagged cases that were not “..on any material credit obligation ..” - is the dilution of the estimating and predicting power of the models for the risk components.

Basel[452] does not mention a materiality for the over-limit situation, although common sense would suggest that a materiality might apply. For example, if a customer with an $10000 overdraft reaches a balance of -$10050, must this start the DPD counter ticking? At NNB I found that modest changes in materiality in these cases made an enormous difference to the default analytics - changing the bad rates by significant factors. The real cause was that the bank didn’t credit-manage this particular product in a way concordant with Basel principles: the issue was resolved by changes to the product, which were in any case appropriate to align business practices with risk issues.

Using a percentage (of limit) as a materiality is a sensible idea on standard products, but can produce unexpected results on large datasets where there will often be some data oddities like limits of $1. Percentage supplemented by an absolute dollar minimum and maximum should provide belt & braces for these situations.