Machine Learning in the default prediction of credit portfolios: the extra advantage

Aug 2, 2026

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This paper investigates how applying machine learning to predict default in credit portfolios changes downstream portfolio risk assessment. Using a large dataset of credit card holders, it embeds the dependence among obligors’ defaults and shows that logistic regression underestimates joint losses and consequently key risk measures, including Value at Risk (VaR) and Expected Shortfall (ES). Robust VaR and ES bounds are derived under a Bernoulli mixture framework that covers traditional structural and reduced-form models.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages32

Reading Time1 h 21 min

AccessFree to download

Abstract

Introduction

Univariate default prediction and ML alternatives

Portfolio-level risk measures (VaR, ES) and dependence

Bernoulli mixture model for joint default

Research setup and organization

arXiv :2205 .01524v2 [ q-fin .RM] 4 Sep 2023 Machine Learning in the default prediction of credit portfolios: the extra advantage. M. DORIA Credit Suisse Services AG, Quantitative Analysis & Technology CCM Credit Model Solutions, CQCB 3 . E. LUCIANO 1 ESOMAS Department and Collegio Carlo Alberto, Universit´a di Torino P. SEMERARO Department of Mathematical Sciences G. Lagrange, Politecnico di Torino. September 6, 2023 1 Corresponding author: Elisa Luciano, ESOMAS Department and Collegio Carlo Alberto, Universit´a di Torino. Email: elisa.luciano@unito.it Abstract This paper studies the consequences of using Machine Learning (ML) to predict default in portfolios of credits. We use a large pool of credit card holders to show that ML algorithms, by their very nature, permit to properly embed the dependence of obligors’default. Traditional methods like the logistic regression underestimate the joint losses and the ensuing risk measures: Value at Risk (VaR) and Expected Shortfall (ES) . The result obtains using VaR and ES bounds robust with respect to the model used for joint default modelling and adopting a Bernoulli mixture approach, which already encompasses traditional structural and reduced form models. We consider the superior ability to handle joint-on top of single-defaults the extra and true advantage of ML in default prediction. keywords: Finance; Risk analysis; Bernoulli mixture model; ML methods; credit cards. 1 Introduction The prediction of default both of single and groups of obligors remains one of the important applications of statistical learning and operational research. The prediction for single obligors is traditionally performed using a statistical tool, the first order Logistic Regression (LR) . Machine Learning (ML) techniques have only recently been considered as alternatives. Most of the literature so far has searched for the most accurate ML method for single obligor defaults. This paper studies the consequences of using ML to predict default in large portfolios of credits. We use a pool of credit card holders because their joint-and not only single-default matters to the card issuing company. For each obligor the credit card data gives us a snapshot of a number of covariates ata specific point in time and the default indicator one point in time later. The covariates include socio-economic indicators as well as present and past bill and payment values. Default is assumed to depend on those covariates. As a preliminary analysis, ML and first order LR are used to describe the-respectively non linear and linear-relationship between the covariates and the probability of default for each obligor. As already shown in the literature, the traditional fit measures (accuracy, sensitivity, ROC, AUC, F1) assign a superiority to the ML techniques. The very contribution of the paper consists in showing that the superiority still holds when predicting the loss deriving from the entire portfolio, through its risk measures, VaR and ES. A key point of this result is the availability of VaR bounds, independent of the joint default distribution. Intuitively, superiority depends on the very nature of ML algorithms, which permit to embed the linear and non linear dependence of obligors’ covariates and therefore of their default. Traditional methods like the logistic regression capture only the linear dependence (or a polynomial approximation of the true dependence), underestimate the losses and the ensuing risk measures. We show that capturing correctly the dependence is not only as important as fitting appropriately the marginal default probability, as one could expect, but also that is more important than fitting the higher order moments of the joint loss. The result is the greater the higher is the portfolio dimension, namely the number of obligors it contains. It holds both per se and when comparing the LR/ML risk measures with the VaR and ES bounds. Without loss of generality, together

FAQs

What problem does the paper address in credit risk modeling?

The paper studies the consequences of using machine learning to predict default in credit portfolios, with emphasis on how joint defaults affect portfolio risk measures.

How does ML improve over logistic regression in this setting?

ML better captures dependence among obligors’ defaults, which leads to more accurate joint losses and avoids the underestimation of VaR and Expected Shortfall seen with logistic regression.

What role does the Bernoulli mixture approach play?

It provides a tractable joint default modeling framework, enables analytical VaR/ES bounds that are robust to the joint default modeling choice, and can be simulated effectively for high-dimensional portfolios like credit cards.

Aug 2, 2026

Upload by Finn