Survival Analysis

Towards modelling lifetime default risk: Exploring different subtypes of recurrent event Cox-regression models ArXiv ID: 2505.01044 “View on arXiv” Authors: Arno Botha, Tanja Verster, Bernard Scheepers Abstract In the pursuit of modelling a loan’s probability of default (PD) over its lifetime, repeat default events are often ignored when using Cox Proportional Hazard (PH) models. Excluding such events may produce biased and inaccurate PD-estimates, which can compromise financial buffers against future losses. Accordingly, we investigate a few subtypes of Cox-models that can incorporate recurrent default events. Using South African mortgage data, we explore both the Andersen-Gill (AG) and the Prentice-Williams-Peterson (PWP) spell-time models. These models are compared against a baseline that deliberately ignores recurrent events, called the time to first default (TFD) model. Models are evaluated using Harrell’s c-statistic, adjusted Cox-Sell residuals, and a novel extension of time-dependent receiver operating characteristic (ROC) analysis. From these Cox-models, we demonstrate how to derive a portfolio-level term-structure of default risk, which is a series of marginal PD-estimates at each point of the average loan’s lifetime. While the TFD- and PWP-models do not differ significantly across all diagnostics, the AG-model underperformed expectations. Depending on the prevalence of recurrent defaults, one may therefore safely ignore them when estimating lifetime default risk. Accordingly, our work enhances the current practice of using Cox-modelling in producing timeous and accurate PD-estimates under IFRS 9. ...

The TruEnd-procedure: Treating trailing zero-valued balances in credit data ArXiv ID: 2404.17008 “View on arXiv” Authors: Unknown Abstract A novel procedure is presented for finding the true but latent endpoints within the repayment histories of individual loans. The monthly observations beyond these true endpoints are false, largely due to operational failures that delay account closure, thereby corrupting some loans. Detecting these false observations is difficult at scale since each affected loan history might have a different sequence of trailing zero (or very small) month-end balances. Identifying these trailing balances requires an exact definition of a “small balance”, which our method informs. We demonstrate this procedure and isolate the ideal small-balance definition using two different South African datasets. Evidently, corrupted loans are remarkably prevalent and have excess histories that are surprisingly long, which ruin the timing of risk events and compromise any subsequent time-to-event model, e.g., survival analysis. Having discarded these excess histories, we demonstrably improve the accuracy of both the predicted timing and severity of risk events, without materially impacting the portfolio. The resulting estimates of credit losses are lower and less biased, which augurs well for raising accurate credit impairments under IFRS 9. Our work therefore addresses a pernicious data error, which highlights the pivotal role of data preparation in producing credible forecasts of credit risk. ...

Analyzing Economic Convergence Across the Americas: A Survival Analysis Approach to GDP per Capita Trajectories ArXiv ID: 2404.04282 “View on arXiv” Authors: Unknown Abstract By integrating survival analysis, machine learning algorithms, and economic interpretation, this research examines the temporal dynamics associated with attaining a 5 percent rise in purchasing power parity-adjusted GDP per capita over a period of 120 months (2013-2022). A comparative investigation reveals that DeepSurv is proficient at capturing non-linear interactions, although standard models exhibit comparable performance under certain circumstances. The weight matrix evaluates the economic ramifications of vulnerabilities, risks, and capacities. In order to meet the GDPpc objective, the findings emphasize the need of a balanced approach to risk-taking, strategic vulnerability reduction, and investment in governmental capacities and social cohesiveness. Policy guidelines promote individualized approaches that take into account the complex dynamics at play while making decisions. ...

Deep Attentive Survival Analysis in Limit Order Books: Estimating Fill Probabilities with Convolutional-Transformers ArXiv ID: 2306.05479 “View on arXiv” Authors: Unknown Abstract One of the key decisions in execution strategies is the choice between a passive (liquidity providing) or an aggressive (liquidity taking) order to execute a trade in a limit order book (LOB). Essential to this choice is the fill probability of a passive limit order placed in the LOB. This paper proposes a deep learning method to estimate the filltimes of limit orders posted in different levels of the LOB. We develop a novel model for survival analysis that maps time-varying features of the LOB to the distribution of filltimes of limit orders. Our method is based on a convolutional-Transformer encoder and a monotonic neural network decoder. We use proper scoring rules to compare our method with other approaches in survival analysis, and perform an interpretability analysis to understand the informativeness of features used to compute fill probabilities. Our method significantly outperforms those typically used in survival analysis literature. Finally, we carry out a statistical analysis of the fill probability of orders placed in the order book (e.g., within the bid-ask spread) for assets with different queue dynamics and trading activity. ...