Modelling Credit Risk using Survival Analysis and Bayesian Techniques

Abstract

Credit-granting institutions provide loans to customers, who may sometimes fail to repay their debts, leading to default. To manage this risk, firms use quantitative credit risk management techniques. These methods help them to estimate and regulate credit risk, ensuring that the firm’s risk exposure aligns with its risk tolerance. This contributes to the overall stability of the firm and the broader economy. One of the key metrics estimated through quantitative credit risk management techniques is the Probability of Default (PD), which serves as an input for calculating the Expected Loss (EL). In this thesis, we focus on applying survival analysis techniques to assess the risk of credit default, by calculating the Probability of Default (PD). Survival analysis involves studying subjects over time in anticipation of encountering an event of interest, such as default. We use survival analysis models such as Cox’s proportional hazards model and its extension to mixture cure models. These models have a baseline hazard component, which we estimate by approximating it using a linear combination of different basis functions. We use Markov Chain Monte Carlo (MCMC) techniques with Hamiltonian Monte Carlo sampling for the Bayesian analysis of these models. We apply these models to both Bondora credit data and German credit data, comparing them with traditional estimation procedures such as partial likelihood maximization and the EM algorithm. To evaluate the predictive performance, we discuss the use of ROC curves and the adjustments required for ROC curves when dealing with censored data.