Default weighted survival analysis to directly model loss given default

Abstract

Traditionally when predicting loss given default (LGD), the following models can be used: beta regression, inverse beta model, fractional response regression, ordinary least squares regression, survival analysis, run-off triangles and Box–Cox transformation. The run-off triangle method is commonly used in practice.

When using survival analysis to model LGD a standard method to use is exposure at default (EAD) weighted survival analysis (denoted by EWSA). This article will aim to enhance the survival analysis estimation of LGD. Firstly by using default weighted LGD estimates and incorporating negative cash flows and secondly catering for over-recoveries. We will denote this new method to predict LGD as the default weighted survival analysis (DWSA). These enhancements were motivated by the fact that the South African Reserve Bank requires banks to use default weight LGD estimates in regulatory capital calculations. Therefore by including this into the survival analysis approach, the model is aligned more closely to regulations. Recovery datasets used by banks include both negative and over-recoveries. By including these into the LGD estimation, the models more are closely aligned to the actual data. The assumption is that the predictive power of the model should therefore be improved by adding these changes. The proposed model is tested on eight datasets. Three of these are actual retail bank datasets and five are simulated. The datasets used are representative of the data typically used in LGD estimations in the South African retail environment.

This article will show that the proposed DWSA model outperforms the EWSA model by resulting in not only the lowest mean squared error (MSE), but also the lowest bias and variance across all eight datasets. Furthermore, the DWSA model outperforms all other models under review.