A Bayesian Hierarchical Model for Unsecured Loan Loss Given Default

• Activity Number: 141
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Katarzyna Bijak*
• Companies: University of Southampton
• Keywords: Bayesian hierarchical model ; Loss Given Default ; regression models

Abstract

Loss Given Default (LGD) is the lender's loss on a loan due to the customer's default, i.e. failure to meet the credit commitment. Modelling LGD for unsecured retail loans is often challenging. In the frequentist two-step approach, the first model (logistic regression) is used to separate positive values from zeroes and the second model (e.g. linear regression) is employed to estimate these values. The models are estimated independently, but they need to be combined to predict LGD, which may be found problematic. The frequentist approach produces a point estimate of LGD for each loan. Alternatively, LGD can be modelled using Bayesian methods. In the Bayesian framework, a single hierarchical model is developed. This makes the proposed approach more coherent. The Bayesian model generates an individual predictive distribution of LGD for each loan. Potential applications of such distributions include approximating the downturn LGD and stress testing LGD under the Basel Accords. As an illustration, the frequentist approach and Bayesian methods are applied to the data on personal loans provided by a large UK bank.