Dependent Credit Default Risk Modelling Using Bernoulli Mixture Models

Misile Kunene ,Joseph Mung’atu ,Euna Gesare Nyarige

doi:10.11648/j.ajtas.20211003.12

Misile Kunene , Joseph Mung’atu + Show 1 more

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https://doi.org/10.11648/j.ajtas.20211003.12

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Abstract

Generalized Linear Mixed Models (GLMMs) can be used to model the occurrence of defaults in a loan or bond portfolio. In this paper, we used a Bernoulli mixture model, a type of GLMMs, to model the dependency of default events. We discussed how Bernoulli mixture models can be used to model portfolio credit default risk, with the probit normal distribution as the link function. The general mathematical framework of the GLMMs was examined, with a particular focus on using Bernoulli mixture models to model credit default risk measures. We showed how GLMMs can be mapped into Bernoulli mixture models. An important aspect in portfolio credit default modelling is the dependence among default events, and in the GLMM setting, this may be captured using the so called random effects. Both fixed and random effects influence default probabilities of firms and these are taken as the systemic risk of the portfolio. After describing the model, we also conducted an empirical study for the applicability of our model using Standard and Poor’s data incorporating rating category (fixed effect) and time (random effect) as components of the model that constitute to the systemic risk of the portfolio. We were able to find the estimates of the model parameters using the Maximum Likelihood (ML) estimation method.

Highlights

From the literature, there is enough evidence that credit default events show significant dependence
We show how these constraints can be applied by estimating model parameters from historical default data using maximum likelihood methods
There are other methods that have been proposed in literature but in this work, we focus on the Maximum Likelihood (ML) method

Summary

Introduction

There is enough evidence that credit default events show significant dependence. One of the stylized facts about credit default data is that periods with many defaults are generally preceded and followed by other periods with many defaults and this has been presented clearly in McNeil and Wendin [1]. Credit contagion is another issue of interest that affects credit defaults; Egloff [2] and Gieseck and Weber [3, 4] for detailed discussions.

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