ECL for short term lending

[Peter Carlsson]

Is there any best practice for calculating PD for the shorter periods?
In the example with 1 day left on a loan calculating like this does not seem realistic:
12-month PD * days / 365

[Marek Muc]

Hi, I've split your post into a separate topic, feel free to provide more background information and context

[JRSB]

presumably you'd already know with certainty if it had defaulted by the time you prepare the financial reports..?

[Peter Carlsson]

Hi,

I'm just a programmer so my understanding of this is not the best. I'm trying to figure out the standard way (if there is one) of calculating ECL when the remaining lifetime is less than 12 months.

We can use an example of a 24 month loan and a 12-month PD of 2% in bucket 1.
The PD part in the ECL calculation gets smaller the closer to the due date it gets, right? How much?
24 months remaining: PD = 12-month PD = 2% (correct right?)
12 months remaining: PD = 12-month PD = 2% (correct right?)
6 months remaining: PD = 12-month PD * 6 / 12 = 1% (is this reasonable?)
1 month remaining: PD = 12-month PD * 1 / 12 ~ 0,16% (this seems optimistic?)
0 months remaining: PD = 12-month PD * 0 / 12 = 0% (this is definitely unrealistic)

I'm sorry if it's not clear or if I'm asking for something that doesn't make sense. I'm thankful for any help i can get.

[JakobLavrod]

Hi!
Great question. From context I guess that what you have is some form of 12m PD model. When computing PD for other horizons outside of 12m, one need to make some sort of assumption (unless one wants to go back to the data and train a new model). One simple such assumption is that the default risk is assumed to be distributed evenly over time, that is, the risk per unit time, called hazard, is constant. The probability to survive a time t is then exp(-hazard*t) (smaller the longer time is). Hence since probability to survive 1y is 1 - PD12 = exp(-hazard). Then, exp(-hazard*t) = [exp(-hazard)]^t = [1 - PD12]^t, hence:
PD(t) = 1 - [1 - PD12]^t

Notice that if t = 1, you get back PD(12) = PD12. Is this a perfect solution? No, it hinges on the constant hazard assumption, but in absence of building a new model, it can often take you quite far.

[Peter Carlsson]

Thank you so much for the response!
Yes the model is for 12m PD.
PD(t) = 1 - [1 - PD12]^t makes a lot of sense until t is close to 0. Is there a common way to avoid PD going to 0 on due date while still using a 12m PD model?

[JakobLavrod]

This is a great question. In general, as JRSB writes, the assumption is that if you are at the due date, the probability should be 0 since there is no time for the status to change. The issue however might be if the company does not have the capability to repay, for example bullet loans. Here it matters alot what the loan structure is. For an amortizing loan where the final payment is quite immaterial and is due "today", I doubt this would be a material effect, but for bullet loans where the last payment is large, one might argue that the PD12 should not really be lowered (since the final payment is within 12m) and just kept constant.

[Marek Muc]

Interesting topic! I’d say that PD decreases as we near the repayment date, mainly because the likelihood of external risks such as economic downturns or geopolitical unrest lessens. But risks specific to the borrower remain unknown to the lender, so we shouldn’t assume these are nearly zero a day before repayment is due. This reminds me of the 'Incurred But Not Reported' (IBNR) concept used in insurance, where it’s acknowledged that insurance events cannot be precisely identified at the reporting date.

[JRSB]

Jackob, good point about bullet loans, maybe there's 1 day left but actually there is no record of payments being made, as none were due until the last day. I guess that makes monitoring much more complex as you have no observable information. I guess you obtain even more evidence in these cases, eg monitoring of financial performance/cash holdings etc in order to inform the ECL models?

[Peter Carlsson]

Thanks for all the great responses!
It looks like different approaches for amortization loans and bullet loans can be useful.

1. Amortization loans
PD closes in on 0. What is a good way of avoiding it actually becoming 0? One way could be to check when the last amortization was made instead of comparing "today" with due date, is there a better way?

2. Bullet loans
PD stays at PD12 or decreases a little bit because of external factors. I could argue that we know a bit about the borrower if time passes and interest is paid monthly and they don't get any external payment remarks etc.
Is the decrease too small to be taken into account? How would it be calculated?

[JakobLavrod]

1. Yes, if the customer has 1 payment left, I would just use PD(1m) = 1 - [1 - PD12]^(1/12), that will give you a non-zero number.

2. One has to be incredibly careful in dealing with bullet loans. For example, for SICR assessment you should never use PD12, but has to use PD lifetime. If I was to be practical, I would argue to look at past data to see how common it is that you have defaults due to the bullet. So for example, in the last 12m, how many of the defaults are actually coming from the last month. Then a simple solution is to weight the hazard so that it is x times more likely for default at the final months. Also bear in mind that if this for example are loans which tend to be refinanced, the bullet payment risk assessment has to be done assuming that the company would NOT extend the loan, as you otherwise distort the risk calculation (no one would default if they never had to pay )