An investigation into Loss Given Default modelling and Economic Capital for Recovery Risk

PhD (Risk Analysis), North-West University, Potchefstroom Campus

Risk management in the credit risk environment has advanced considerably over the last few decades. During the same time, statistical models developed for this purpose have grown in variety and sophistication. Initially, statistical models focused on the assessment of a counterparty’s creditworthiness (i.e. default risk), but the modelling of the recovery process and outcome after default are receiving more and more attention. Loss Given Default (LGD) represents the loss suffered on a loan, expressed as a percentage of the exposure amount at default. The LGD is one of the key risk parameters used in determining a bank’s regulatory capital under the Basel Capital Accords. This thesis comprises three articles, each making a unique contribution to a different aspect of the modelling of LGD. In the first article, a methodology for determining an LGD discount rate is proposed. The methodology infers a discount rate from a market-consistent, or fair, price for defaulted exposures, inspired by the Solvency II regulatory regime’s cost of capital approach. The main drivers of the LGD discount rate are found to be the mean and variance of recovery cash flows. The discount rate is also shown to be sensitive to the bank’s cost of equity, particularly when recovery rates are low. It is demonstrated that this discount rate reflects the non-diversifiable risk inherent in the recovery cash flows and therefore satisfies the principles established by the banking regulator. In the second article, two alternative models are proposed to better capture the bimodality of LGD data, and to reduce the difference between the empirical and distributional means, where the distributional mean is the expectation of the fitted parametric model. Both proposed models are mixtures of standard power distributions and outperform the benchmark beta distribution in terms of reducing bias in the estimation of the mean LGD. In this way, better alignment between a bank’s Regulatory Capital and Economic Capital models can be achieved. In the third article, an improved survival modelling approach for modelling the time to loan writeoff is proposed. This approach includes a frailty component in the promotion time cure model. The frailty parameter accounts for common unobservable factors and possible observable covariates not in the model. The proposed models include gamma and inverse Gaussian distributed frailty parameters, as well as a shared frailty model. The finite sample performance of maximum likelihood estimation is analysed through a Monte Carlo simulation study, after which the models are applied to a simulated data set, as well as a real-world loan loss data set. The gamma frailty model produces the best fit to the data and allows for the modelling of a non-monotone shape of the hazard function. Additionally, the shared frailty term included accounts for the dependence between the failure times of individual subjects within a cluster, leading to more accurate estimates of hazard rates and write-off times. The proposed models offer an attractive alternative approach to modelling the probability of loan write-off in two-step LGD models. Overall, this study should contribute to the development of more accurate and robust credit risk models, specifically in relation to LGD, which are essential for the effective management of credit risk in financial institutions.

Doctoral