Dynamic multi-state delinquency models: incorporating repeated events, stress testing analysis and multiple lending products

Abstract

Credit risk modelling has become crucial for impairment and capital calculations. Every day, financial institutions deal with internal and regulatory requirements to determine and assess the components that influence their portfolios’ performance. For a lending portfolio, understanding the stages and dynamics of the borrowers’ journey towards a potential default, plays a key role in determining their risk profile. This research is centred around the estimation and prediction capabilities of multi-state delinquency models that help characterise movements between different stages of the repayment performance of a loan over time. In contrast to traditional credit scoring models that estimate the probability of default (normally defined as 90 Days Past Due (DPD)), we consider earlier states of 30 DPD and 60 DPD that may lead to a potential default. These interim states can act as early warnings to lenders, and the knowledge about expected time spent in different states are particularly useful for planning. Dynamic multi-state models (a time-to-event framework) are suitable for this type of modelling as they are able to infer the time a financial instrument will spend on a given repayment state before moving out of it, while they allow us to include censored data, time-independent covariates and time-dependent covariates. Specifically, and to anticipate future losses, this thesis addresses the following questions. How long will it take a borrower to re-enter the delinquent book for the second time? and for the third time? Do stressed macroeconomic factors have an impact on recurrent transitions? If a borrower under-performs in one lending product, how long will it take to miss a payment in another product? In seeking a response to these questions, this thesis makes five contributions to knowledge. First, we estimate a multi-state delinquency model for a portfolio of residential mortgages considering six types of transitions. Second, we explicitly incorporate and quantify the impact of recurrent events on these estimations. Third, we develop a methodology to predict scenario-conditional transition intensities beyond the lag of the time-varying covariates for a multi-state model. Fourth, we link the repayment performance of alternative credit lines an individual holds. Fifth, we assess the predictive performance of multi-state delinquency models using time-varying AUROCs. We propose a dynamic multi-state delinquency model to estimate and predict transition probabilities between any repayment states and between any two points in time based on account-level application and behavioural data. Macroeconomic characteristics are also incorporated. For the first time, this methodology is applied to a retail mortgage portfolio while considering six plausible types of transitions. Moreover, the impact of recurrent events is explicitly quantified and three alternative methodologies are applied for comparison purposes. We show that these methods present similar results in terms of variable selection and that the estimated transition probabilities are accurate for the up to date book but tend to overestimate the movements towards delinquency. Stress testing and IFRS9 are topics widely discussed by academics and practitioners. We combine the dynamic multi-state models previously mentioned with macroeconomic scenarios to estimate a stress testing model that forecasts delinquency states and transition probabilities at the borrower level for a mortgage portfolio. Specifically, we enhance the existing methodology in the literature by estimating scenario-specific forecasts beyond the lag of time-dependent covariates which enable us to not only predict a complete path of transition probabilities under alternative macroeconomic scenarios but to predict which specific accounts will be under each repayment state in the future, also conditional on the scenario. This flexibility is crucial for forecasting stage allocation distributions, a requirement for stress testing exercises under IFRS9. We show that the estimated transition intensities are sensitive to the assumptions behind a macroeconomic scenario, that severe economic conditions affect younger vintages the most, and that the relative impact of the stress scenario differs by attributes observed at origination. Finally, we expand the estimation of transition intensities between repayment states by considering multiple accounts belonging to the same customer, together with recurrent events and discontinuous risk intervals. Generally, academic research focuses on analysing one product at a time and misses the inter-dependencies between credit lines belonging to the same customer. In this thesis, and leveraging on dynamic multi-state models, we explicitly estimate the impact that the performance on one account has on another one that an individual also holds. We compare the results with model specifications that do not account for such a link by comparing time-specific AUROCs with alternative definitions of cases and controls. We conclude that incorporating the repayment performance of an alternative product the individual also holds contributes to enhanced estimates of transition intensities as the predictive accuracy tends to outperform the results observed for models with no link.