Contribuciones a los modelos multivariantes internos de riesgo de crédito, acordes con Basilea II.

Resumo

In this theses we introduce the Hybrid Linear Logistic Models based on Linear Expansions of Basis Functions (HLLM models), obtained by expanding the non linear component of the Partially Linear Logistic Models, PLLM. Linear expansions of the basis functions, specific for each variable, are used. A supervised constructive method to select the basis functions that configure the structure of the model, is also proposed. The selection procedure is based on the goodness of fit, explanatory power, discriminatory power, and efficacy of the classification for each component. The General Estimation Problem for Logistic Models based on linear expansions of Basis Functions is stated and solved using the linear expansions of the basis functions to configure the objective function, the logistic loss as criteria for goodness of fit and the penalization functional as regularization term. A general unified framework that includes most of the more recent credit scoring models, by formalizing their functional structures as linear expansions of the base functions for the explanatory variables of the credit risk, is presented. The proposed models are classified in four groups: probability, logistic, probit and support vector models (based on linear expansions of base functions). All the previous contributions are applied for developing a credit scoring proactive HLLM model based on real data (77.602 individuals and 63 credit risk variables) obtained from a Spanish Financial Institution. We use the IRB approach of the second Basel Accords.