Accounting for prepayments in CECL: Part 2

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Last week, we kicked off this two-part series by discussing how Visible Equity’s loss curve model for CECL implicitly incorporates prepayment information. Today, we’ll wrap up the discussion by talking prepayments in the context of probability of default (PD). At the risk of sounding like a broken record, I’m going to re-quote a statement about prepayments from the standards update

 

An entity shall consider prepayments as a separate input in the method or prepayments may be embedded in the credit loss information in accordance with paragraph 326-20-30-5.

 

As was explained in the Part 1 article, this means that a model needs to either implicitly “embed” prepayments, or prepayments need to be added to the model as a separate input. We concluded that the loss curve model is an example of one that implicitly considers prepayments. Is this also true of the PD model? Let me tell you a story.

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Fig 1: Grandmother CECL

 

It all begins with disease. Not really, but just go with me. Imagine you’re running a study on the effects of drug x on the dastardly disease y. You find 500 patients diagnosed with disease y to participate in the study, in which half will receive drug x, and half will receive an alternate, standard drug. The patients agree to check in weekly for 25 weeks. At various points throughout the 25 weeks, some of the patients pass away, and you mark their “survival time” in weeks from the beginning of the study, for the purpose of determining whether or not drug x is more effective in increasing survival time than the standard treatment. This comparison would seem to be a fairly simple task if it weren’t for a couple of things:

  1. Some patients will “drop out” of the study before its completion, making it impossible to know if and when the patient passed away
  2. Some patients will survive to the end of the study, but that doesn’t mean they will not eventually die from the disease

These complications are cases of “right censoring.” That is, we know a patient survived to a certain point, but we have no data beyond that point. Censored data necessitates special methodologies, many of which fall under the umbrella of Survival Analysis. One such method, the Cox proportional hazard model, is very well developed, and fairly easy to implement.

 

Okay, now let’s think about this study in terms of loans instead of patients. In Visible Equity’s database, we have tens of millions of loans. Our goal for the PD model is to use that data to build a predictive model relating loan/economic characteristics to the likelihood of defaulting. We have the means of observing how long each loan “survives,” as well as the time-specific loan attributes throughout the life of the loan. Similar to the situation where a patient survives to the end of the study, we have loans in our database that are currently active, and thus are “right-censored” since we can’t know with certainty whether or not the loan will eventually default. Can you see the parallels? It seems natural that the methods used to model patient survival can also be used to model loan survival. But here’s the thing. Prepayments throw a huge, ginormous WRENCH in the whole thing, and here’s why. Many people, including a younger version of myself, believe that prepayments should also be considered “right-censored” data points, just like those patients who dropped out of the study. But there is a key difference. Patients who drop out of the study still have the possibility of dying from the disease. Prepaid loans, on the other hand, will deterministically never default. With. 100%. Probability. Since the standard Cox model is built around those dropped-out patients who may still die, it is not equipped to accommodate prepaid loans that will never default.

 

To deal with prepayments we must consider a modified Cox model, known as a competing hazard model. This allows for the possibility of multiple competing events (i.e. a situation where, if one event occurs, the other cannot). In the medical example, suppose treatment x carries the risk of heart attack (with the heart attack being completely unrelated to disease y). Patients who die of a heart attack as a result of taking drug x will never die of disease y, just as prepaid loans will never default. Both events are of interest. Both events must be considered possible. Both events need to be incorporated into the model.

 

Visible Equity’s competing hazard model does just this. During each month of a loan’s life, we model the competing probabilities of default, prepayment, and remaining current. So yes, in a proper competing hazard model, prepayments are implicitly considered.


Rachel Messick

Product Manager/Data Scientist at Visible Equity


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