Preparing for Basel II: Common Problems, Practical Solutions: Part 4: Time to Default
Morrison, Jeffrey S., The RMA Journal
Previous articles in this series have focused on the problems of missing data, model-building strategies, and special challenges in model validation--topics often associated with modeling retail portfolios. This article moves a bit beyond Basel, offering additional tools to further enhance risk and account management strategies. Building a quantitatively based framework--beyond any Basel II requirements--is just plain old good risk management.
Banks opting for advanced status under Basel II are expected to have, among other things, models for PD (probability of default) and LGD (loss given default). Some of these models will be provided by outside vendors, while others will be more custom driven. Previous articles in The RMA Journal have discussed how to build both PD and LGD models. (1) A PD model will let you know the probability of a loan defaulting sometime in the next year. Looking at the modeling results, you might think that loans with an estimated PD of .95 will default more quickly than ones with a PD of .45 or lower. The PD model, however, was never designed to address this issue. Such a model makes no attempt at describing the exact timing of default--either within the year or further down the road. Wouldn't it be nice to know--at booking or at any time during the life of the loan--when the default might occur? Obviously, if the loan were expected to default in the next few months it would not be worth your while to book it. But what if you knew that the probability of default for a particular loan might stay low for the first three years but increase dramatically thereafter? Would it be worthwhile then to know? Under what conditions might you book it?
Modeling time to default requires nothing but a slight variation to a statistical technique already discussed in previous articles. Although building a good time-to-default model can prove challenging, your success with PD and LGD models, coupled with a comprehensive and well-understood database, should give you a great head start. If successful, your organization will have a mechanism to help predict when an account will default--a prediction made early enough that it might prevent the loss from occurring, mitigate its impact if it does occur, or at the very least provide insight into the profitability, pricing, or term structure of the loan. For illustration purposes and to keep things simple, we will use a hypothetical dataset with generically labeled variables called X1, X2, and X3. In reality, these might be predictors such as LTV, debt to income, fixed-versus-variable interest rate, term of loan, and so forth.
Let's start with a story. Three economists went deer hunting. The first economist saw a deer and shot to the left of the animal, missing it by about two feet. The second economist shot to the right of the deer, missing it by about the same margin. Immediately afterwards and with unbridled enthusiasm, the third economist stood up and shouted, "We got him, we got him!!" The idea here is that economists who focus on predicting when an event will occur (such as a downturn in the economy) realize the difficulty of their task. They are happy simply when they come close. Whereas previous articles in this series looked at methods of predicting if an account will default sometime within a 12-month window of time, we now consider a more formidable task--the timing of default.
Censored Data and Survival Analysis
The task is more formidable for two reasons. First, obtaining a certain level of accuracy across time is inherently far more difficult than in simpler classification methods. In other words, it's much harder to explain various degrees of gray than to explain an object being either black or white. Therefore, a higher standard of predictive data may be required. The second reason deals with censoring--a data issue where important information is not available or is present only outside the study period. Given that the data collection efforts for any study cover a specific period, there will be many accounts whose final default status you will not know. …