You are currently browsing the tag archive for the ‘cumulative density function’ tag.
What shape does a typical default hazard curve have?
Note that this post is about default hazard – the churn hazard curve is a completely different matter.
Recall that the hazard at any particular MOB is indicating the instantaneous chance that a good account of that MOB age might go bad. So, where the curve is highest is showing the most dangerous age for accounts.
For most products, the hazard will be very close to zero for the first 3 or 4 months. This depends on the details of your default definition, but for example a simple 90DPD type of definition can’t produce a default in MOB 1,2 or 3. Some default definitions can be triggered even in those first MOBs via business rules about bankruptcy etc.
For some situations – like a new product to market – there can be an issue of “application fraud” or “soft fraud” whereby new accounts come on book that perhaps never had an intention to make any repayments. Such a situation would show up as a spike in hazard around the 4-5 MOB.
Aside from application fraud, typical CC hazard curves tend to rise rapidly to a maximum by 9-12 MOB and then to decline slowly to stable plateau at maybe half the peak hazard level. Hazard doesn’t decline to zero because no matter how old an account is, there remains a residual chance that it can go into default.
In practice, one gets relatively little chance to study the hazard behaviour at long MOB – say, over 36 months – because that calls for data going back more than 3 years – rather a long time in credit markets.
On a technical point, a constant hazard corresponds to an exponential distribution for the waiting time until first default.
It would be fairly easy to confuse the notions of hazard curve and probability density function, since (for default on a typical credit product) both start at zero and climb to a peak and then decline.
The more data used in the analysis, the smoother the curves will be, but whatever the case the cumulative density function (“emergence curve”) will always be much smoother than the hazard and pdf.
For the reasons in the above two paragraphs, I recommend presenting default analytical work via the cdf graph using a non-technical name like “emergence curve” or “default profile”. Please send in your preferred nomenclatures in case there is some consensus we could publicise. My slight preference is for “default profile” which is neutral and non-technical and easily accommodates “churn profile” or “cross-sell profile” when one analyses some other waiting time quantity such as these.
The above paragraph is about presenting and communicating the results; but for analytical insight, I recommend that the analyst should be looking at the hazard curves as well – for discussion next time.