Discrete-Time Survival Models with Neural Networks for Age–Period–Cohort Analysis of Credit Risk

Hao Wang, Anthony Bellotti, Rong Qu, Ruibin Bai

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)


Survival models have become popular for credit risk estimation. Most current credit risk survival models use an underlying linear model. This is beneficial in terms of interpretability but is restrictive for real-life applications since it cannot discover hidden nonlinearities and interactions within the data. This study uses discrete-time survival models with embedded neural networks as estimators of time to default. This provides flexibility to express nonlinearities and interactions between variables and hence allows for models with better overall model fit. Additionally, the neural networks are used to estimate age–period–cohort (APC) models so that default risk can be decomposed into time components for loan age (maturity), origination (vintage), and environment (e.g., economic, operational, and social effects). These can be built as general models or as local APC models for specific customer segments. The local APC models reveal special conditions for different customer groups. The corresponding APC identification problem is solved by a combination of regularization and fitting the decomposed environment time risk component to macroeconomic data since the environmental risk is expected to have a strong relationship with macroeconomic conditions. Our approach is shown to be effective when tested on a large publicly available US mortgage dataset. This novel framework can be adapted by practitioners in the financial industry to improve modeling, estimation, and assessment of credit risk.

Original languageEnglish
Article number31
Issue number2
Publication statusPublished - Feb 2024


  • age–period–cohort
  • credit risk
  • neural network
  • survival model

ASJC Scopus subject areas

  • Accounting
  • Economics, Econometrics and Finance (miscellaneous)
  • Strategy and Management


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