Modelling LGD using Bayesian methods

Bijak, Katarzyna and Thomas, Lyn C. (2011) Modelling LGD using Bayesian methods. Credit Scoring and Credit Control XII conference, Edinburgh, United Kingdom. 23 - 25 Aug 2011.

Abstract

In this research, LGD is modelled using Bayesian methods. The LGD distribution usually has a high peak at zero, since there are many customers who default but finally pay in full. Therefore, LGD is often found difficult to model. In the traditional, two-step approach, two separate models are estimated independently, which can be considered problematic from the methodological point of view. The first model (logistic regression) separates positive values from zeroes, whereas the second model (e.g. linear regression) allows for the estimation of the positive values. The result is a point estimate of LGD for each customer. In order to apply the traditional approach, one has either to set a cut-off for the first model or to calculate a product of the estimated value and probability that this value is greater than zero. One can also draw from a Bernoulli distribution with the estimated probability, whether to assign the value or zero (this is equivalent to using a random cut-off). Alternatively, both applications (probability-times-value and random cut-off) can be described with graphs and modelled using Bayesian graphical models. In the Bayesian framework, one can build a single, hierarchical model instead of two separate ones. Thus, this is a coherent approach. As far as the estimation results are concerned, there is an individual predictive distribution of LGD for each customer, rather than just a single number. Having a distribution, one can use its various characteristics such as mean, median and other quantiles. The distributions can be used, for example, to estimate the downturn LGD under the new Basel Accord. In this research, the Bayesian models as well as the traditional approach are applied to the data on personal loans provided by a large UK bank.

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Contributors

Author: Katarzyna Bijak

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