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Testes de homogeneidade e heterogeneidade para os modelos de Loss Given Default (LGD)
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Resumo(s)
This project aimed to evaluate the segmentation of Loss Given Default (LGD) models, specifically their statistical robustness. The methodology applied was based on two fundamental principles: ensuring homogeneity within the final segments and ensuring heterogeneity between the final segments, in order to guarantee that the final segments are consistent in terms of customer differentiation and risk profile. To ensure homogeneity, it was established that segments with a standard deviation greater than 100% would be considered non-homogeneous, recommending further analysis and a possible revision of that segment. This analysis considered a statistical criterion whereby a division would only occur if the risk driver presented a p-value equal to or less than 5%. It is also important to mention that any possible disaggregation of segments must comply with the predefined definitions for each final segment, such as a minimum number of observations of 800 in that segment. Regarding heterogeneity, the objective was to identify segments with identical risk profiles for which there is no reason to remain disaggregated. Initially, the variance of each group of segments under analysis was examined, using the F-test to assess the equality of variances, in order to apply the most appropriate statistical test. When the two segments analyzed had equal variances, the T-test was applied to compare the means; otherwise, Welch's test was used, suitable for unequal variances. Finally, the discriminatory power was analyzed using the gAUC (generalized Area Under the Curve) performance metric of the proposed model, and it was compared with the model currently in use at the institution. The results show that the segmentation obtained with this project demonstrates better performance when compared to the segmentation currently utilized.
Descrição
Trabalho de Projeto de Mestrado, Matemática Aplicada à Economia e Gestão, 2025, Universidade de Lisboa, Faculdade de Ciências
Palavras-chave
Loss Given Default Segmentation Homogeneity Heterogeneity Discriminatory Power