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Overview of Exposure at Default Models

Exposure at default (EAD) is the loss exposure (balance at the time of default) for a bank when a debtor defaults on a loan.

For example, the loss reserves are usually estimated as the expected loss (EL), given by the following formula:


With increased availability of data, there are several different types of EAD models. Risk Management Toolbox™ supports:

  • Regression models — These are linear regression models where the response is a transformation of the EAD data. For more information on the supported transformations, see Regression.

  • Tobit models — These are censored regression models with explicit limits on the response values. Censoring on the left, right or both sides are supported. For more information, see Tobit.

  • Beta models — These are beta regression models with explicit limits on the response values. Censoring on the left, right or both sides are supported. For more information, see Beta.

Model Development and Validation

Risk Management Toolbox supports the modeling and validation of EAD models through a family of classes supporting:

The supported model types are Regression, Tobit, and Beta models.

A typical modeling workflow for EAD analysis includes:

  1. Data preparation

    Data preparation for EAD modeling requires a significant amount of work in practice. Data preparation requires consolidation of account information, pulling data from multiple data sources, accounting for recoveries, direct and indirect costs, determination of discount rates to determine the observed EAD values. There is also work regarding predictor transformations and screening. There is a wide range of tools available to treat missing data (using fillmissing), handle outliers (using filloutliers), and perform other data preparation tasks. The output of the data preparation is a training dataset with predictor columns and a response column containing the EAD values.

  2. Model fitting

    Use the fitEADModel function to fit an EAD model. You must use the previously prepared data and select a model type. Optional inputs allow you to indicate the limit (LimitVar) and drawn (DrawnVar) values for a Regression, Tobit, or Beta model. The limit value depends on the loan. If its a credit card, the limit is the credit limit, and if this is a mortgage limit it is the initial loan amount. In general, LimitVar is the maximum amount that can be borrowed. DrawnVar is the balance on the account at the time of observation, prior to default and EAD is the balance at the time of default. Also, you can specify a model description and also specify a model ID or tag for reporting purposes during model validation.

  3. Model validation

    There are multiple tasks involved in model validation, including

    • Inspect the underlying statistical model, which is stored in the 'UnderlyingModel' property of the Regression, Tobit, or Beta object.

    • Measure the model discrimination on either training or test data with the modelDiscrimination function. Visualizations are generated using the modelDiscriminationPlot function. Data can be segmented to measure discrimination over different segments.

    • Measure the model calibration on either training or test data with the modelCalibration function. Visualizations are generated using the modelCalibrationPlot function. Also, you can visualize the residuals.

  4. Once you develop and validate an EAD model, you can use it for lifetime ECL analysis. The Expected Credit Loss Computation example and portfolioECL demonstrates the basic workflow for computing ECL.


[1] Baesens, Bart, Daniel Roesch, and Harald Scheule. Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS. Wiley, 2016.

[2] Bellini, Tiziano. IFRS 9 and CECL Credit Risk Modelling and Validation: A Practical Guide with Examples Worked in R and SAS. San Diego, CA: Elsevier, 2019.

[3] Brown, Iain. Developing Credit Risk Models Using SAS Enterprise Miner and SAS/STAT: Theory and Applications. SAS Institute, 2014.

[4] Roesch, Daniel and Harald Scheule. Deep Credit Risk. Independently published, 2020.

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