Electronic Thesis and Dissertation Repository

Thesis Format



Doctor of Philosophy


Statistics and Actuarial Sciences


Reesor Mark R


Wilfrid Laurier University

2nd Supervisor

Metzler Adam


Wilfrid Laurier University

Joint Supervisor


The provision in Paragraph 468 of Basel II Framework Document for calculating loss given default (LGD) requires that parameters used in Pillar I of Basel II capital estimations must be reflective of economic downturn conditions so that relevant risks are accounted for. This provision is based on the fact that the probability of default (PD) and LGD correlations are not captured in the proposed formula for estimating economic capital. To help quantify economic downturn LGD, the Basel Committee proposed establishing a functional relationship between long-run and downturn LGD.

To the best of our knowledge, the current proposed models that map out this relationship have the same underlying framework. This thesis presents a general factor PD-LGD correlation model within the conditional independence framework, where obligors’ defaults are conditional on a common state of affairs in the economy. We highlight a mistake that is frequently made in specifying loss given default, which is, current studies ignore the difference between account-level potential loss and LGD. By correcting this mistake and deriving the correct distribution of potential loss and LGD, sensitivity analysis is conducted to ascertain the impact of the defective model on economic capital and parameter estimates. The relationship between the account and portfolio level correlations are explored. Finally, an empirical analysis is conducted to validate the proposed estimation scheme of parameters in the model.

Summary for Lay Audience

When Banks issue loans, they are required to set aside some funds to protect the credit issued in case of default. These funds are termed economic capital. It is imperative that the funds set aside adequately protect these positions even in stressful economic conditions. Knowing the right amount of money for this purpose is a concern. Financial Regulators require that the parameters used in estimating economic capital are reflective of bad economic conditions, however, the formula presented in their document does not reflect this. We have shown that existing proposed methods to address this are defective, which implies that the empirical findings based on these methods will be flawed as well. This flaw is fixed and exploratory work conducted.