## Overview of Loss Given Default Models

Loss given default (LGD) is the proportion of a credit that is lost in the event of default. LGD is one of the main parameters for credit risk analysis. Although there are different approaches to estimate credit loss reserves and credit capital, common methodologies require the estimation of probabilities of default (PD), loss given default (LGD), and exposure at default (EAD). The reserves and capital requirements are computed using formulas or simulations that use these parameters. For example, the loss reserves are usually estimated as the expected loss (EL), given by the following formula:

EL = PD * LGD * EAD

Earlier LGD models focused on portfolio-level LGD. The Frye-Jacobs model is a simple parametric model that relates a conditional PD to a conditional LGD value. For more details on this model, see `fryeJacobsLGD`. Its simplicity makes it a useful tool for recent applications such as climate stress testing. For more information, see the example Assess Climate Change Impact on Credit Risk Using UNEP FI Methodology. With increased availability of data and computational power, there are different types of statistical LGD models that can be trained on loan-level data. Risk Management Toolbox™ supports:

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

• Tobit models — These are censored regression models with explicit limits on the response values to capture the fact that LGD can take values only between 0 and 1. 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 to capture the fact that LGD can take values only between 0 and 1. For more information, see `Beta`.

The Model Loss Given Default example shows these two types of models, as well as other models, are fitted using Statistics and Machine Learning Toolbox™. Specifically, besides the regression and Tobit models, this example also includes a non-parametric, look-up table type of model; a Beta regression model; and a “two-stage” model where a classification model (cure-no cure) and a regression model (predicted LGD conditional on no cure) work together to make LGD predictions.

In addition, you can use the `Regression`, `Tobit`, and `Beta` models to develop LGD models that include macroeconomic predictors for stress testing or to support regulatory requirements such as IFRS 9 and CECL. For more information, see Overview of Lifetime Probability of Default Models.

### Model Development and Validation

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

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

A typical modeling workflow for LGD analysis includes:

1. Data preparation

Data preparation for LGD 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 LGD 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 LGD values.

2. Model fitting

Use the `fitLGDModel` function to fit an LGD model. You must use the previously prepared data and select a model type. Optional inputs allow you to indicate which variables correspond to predictor variables, or which transformation to use for a regression model, or the censoring side for a `Tobit` or `Beta` model. 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

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

## References

[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] Gupton, G., and R Stein. "Losscalc v2: Dynamic Prediction of LGD Modeling Methodology". Moody’s KMV Investor Services, 2005.