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
With increased availability of data, there are several different types of LGD models. 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
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
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
Tobit 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.
Risk Management Toolbox supports the modeling and validation of LGD models through a family of classes supporting:
Model fitting with the
Prediction of LGD with the
A typical modeling workflow for LGD analysis includes:
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
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.
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 model. You
can specify a model description and also specify a model ID or tag for
reporting purposes during model validation.
There are multiple tasks involved in model validation, including
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
Validate the model against a benchmark (for example, a champion model). For more information, see Compare Tobit LGD Model to Benchmark Model.
Perform a cross-validation analysis to compare alternative models. For more information, see Compare Loss Given Default Models Using Cross-Validation.
Perform a qualitative assessment of conditional PD
predictions by using the
predict function directly with edge cases.
Visualize residuals using the
modelAccuracyPlot function. There are
examples of additional visualizations using histograms and
box plots in the Model Loss Given Default
 Baesens, Bart, Daniel Roesch, and Harald Scheule. Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS. Wiley, 2016.
 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.
 Gupton, G., and R Stein. "Losscalc v2: Dynamic Prediction of LGD Modeling Methodology". Moody’s KMV Investor Services, 2005.