Semi-structured multi-state delinquency model for mortgage default

We propose a semi-structured discrete-time multi-state model to analyse mortgage delinquency transitions. This model combines an easy-to-understand structured additive predictor, which includes linear effects and smooth functions of time and covariates, with a flexible neural network component that captures complex nonlinearities and higher-order interactions. To ensure identifiability when covariates are present in both components, we orthogonalise the unstructured part relative to the structured design. For discrete-time competing transitions, we derive exact transformations that map binary logistic models to valid competing transition probabilities, avoiding the need for continuous-time approximations. In simulations, our framework effectively recovers structured baseline and covariate effects while using the neural component to detect interaction patterns. We demonstrate the method using the Freddie Mac Single-Family Loan-Level Dataset, employing an out-of-time test design. Compared with a structured generalised additive benchmark, the semi-structured model provides modest but consistent gains in discrimination across the earliest prediction spans, while maintaining similar Brier scores. Adding macroeconomic indicators provides limited incremental benefit in this out-of-time evaluation and does not materially change the estimated borrower-, loan-, or duration-driven effects. Overall, semi-structured multi-state modelling offers a practical compromise between transparent effect estimates and flexible pattern learning, with potential applications beyond credit-transition forecasting.

Joint model for longitudinal and spatio-temporal survival data

In credit risk analysis, survival models with fixed and time-varying covariates are widely used to predict a borrower's time-to-event. When the time-varying drivers are endogenous, modelling jointly the evolution of the survival time and the endogenous covariates is the most appropriate approach, also known as the joint model for longitudinal and survival data. In addition to the temporal component, credit risk models can be enhanced when including borrowers' geographical information by considering spatial clustering and its variation over time. We propose the Spatio-Temporal Joint Model (STJM) to capture spatial and temporal effects and their interaction. This Bayesian hierarchical joint model reckons the survival effect of unobserved heterogeneity among borrowers located in the same region at a particular time. To estimate the STJM model for large datasets, we consider the Integrated Nested Laplace Approximation (INLA) methodology. We apply the STJM to predict the time to full prepayment on a large dataset of 57,258 US mortgage borrowers with more than 2.5 million observations. Empirical results indicate that including spatial effects consistently improves the performance of the joint model. However, the gains are less definitive when we additionally include spatio-temporal interactions.

The Deep Promotion Time Cure Model

We propose a novel method for predicting time-to-event in the presence of cure fractions based on flexible survivals models integrated into a deep neural network framework. Our approach allows for non-linear relationships and high-dimensional interactions between covariates and survival and is suitable for large-scale applications. Furthermore, we allow the method to incorporate an identified predictor formed of an additive decomposition of interpretable linear and non-linear effects and add an orthogonalization layer to capture potential higher dimensional interactions. We demonstrate the usefulness and computational efficiency of our method via simulations and apply it to a large portfolio of US mortgage loans. Here, we find not only a better predictive performance of our framework but also a more realistic picture of covariate effects.