Modelos de mezclas Bernoulli con regresión logística: una aplicación en la valoración de carteras de crédito
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Este trabajo final de maestría, modalidad de profundización, consiste en la elaboración
de un problema de modelación estadística aplicada al sector crediticio. El objetivo es aplicar un modelo de regresión logística o un modelo de aprendizaje de máquina para calcular la probabilidad de default e incorporarla en la fórmula para hallar la distribución de costos totales en el modelo de Mezclas Bernoulli, con el fin de estimar valores de cuartiles superiores de la distribución de los costos totales, denominados la provisión. Para cumplir lo anterior se deben calcular las probabilidades de incumplimiento (o de default) después de realizar una competencia entre modelos vía mejor medida de ajuste (AUC), precisión y rango del intervalo de precisión (IC precisión); si bien el título solo menciona regresión logística, este modelo competirá con modelos de aprendizaje de máquina como arboles aleatorios, bosques aleatorios, Knn y máquinas de soporte vectorial y con el de mejor AUC, precisión y IC precisión se calcularán dichas probabilidades de default. Además, se calcula la distribución aproximada del monto total de las perdidas por incumplimiento para créditos originados entre 2014 y 2018. Tales costos totales se modelan mediante ciertos tipos de sumas de variables aleatorias que se denominan Mezclas Bernoulli para, finalmente evaluar el capital expuesto de una cartera de créditos y así entender el grado de deterioro de esta cartera para créditos originados entre 2014 y 2018. Palabras claves Riesgo de crédito, distribuciones de Mezclas Bernoulli, regresión logística, modelos de aprendizaje de máquina, distribución de perdidas, VaR y TVaR
This _nal master's work, deepening modality, consists in the elaboration of a statistical modeling problem applied to the credit sector. The objective is to apply a logistic regression model or a machine learning model to calculate the probability of default and incorporate it in the formula to _nd the distribution of total costs in the Bernoulli Blends model, in order to estimate values of higher quartiles of the distribution of total costs, called the provision. To accomplish the above, the probabilities of default must be calculated after competition between models via best _t measurement (AUC), precision and precision interval range (IC precision); although the title only mentions logistic regression, this model will compete with machine learning models such as random trees, random forests, Knn and vector support machines and with the best AUC, precision and IC precision these default probabilities will be calculated. In addition, the approximate distribution of the total amount of default losses is calculated for credits originated between 2014 and 2018. These total costs are modeled using certain types of random variable sums called Bernoulli Blends to _nally evaluate the exposed capital of a loan portfolio and thus understand the degree of impairment of this portfolio for loans originated between 2014 and 2018..
This _nal master's work, deepening modality, consists in the elaboration of a statistical modeling problem applied to the credit sector. The objective is to apply a logistic regression model or a machine learning model to calculate the probability of default and incorporate it in the formula to _nd the distribution of total costs in the Bernoulli Blends model, in order to estimate values of higher quartiles of the distribution of total costs, called the provision. To accomplish the above, the probabilities of default must be calculated after competition between models via best _t measurement (AUC), precision and precision interval range (IC precision); although the title only mentions logistic regression, this model will compete with machine learning models such as random trees, random forests, Knn and vector support machines and with the best AUC, precision and IC precision these default probabilities will be calculated. In addition, the approximate distribution of the total amount of default losses is calculated for credits originated between 2014 and 2018. These total costs are modeled using certain types of random variable sums called Bernoulli Blends to _nally evaluate the exposed capital of a loan portfolio and thus understand the degree of impairment of this portfolio for loans originated between 2014 and 2018..