IMPACT ASSESSMENT OF LOSS GIVEN DEFAULT (LGD) MODELS’ RISK ON REGULATORY CAPITAL: A BAYESIAN APPROACH

The model is wrong!” so it is determined. All of the estimated output using the model becomes un-reliable immediately. And so is every other result calculated using the unreliable output. So what is the impact of the model being “wrong” in the later calculations? To address this question, this paper presents a Bayesian approach that provides a quantitative assessment for the impact on downstream results calculated using the unreliable estimates. Section 1 details the practical challenge in the financial industry and discusses why this is important. Section 2 starts the discussion with a description of the overall framework for this Bayesian approach, introducing and defining each individual component. Then Sections 3 and 4 carry on discussing the prior and likelihood distributions, respectively. Section 5 then obtains the target posterior distribution by applying the Bayesian posterior update using obtained prior and likelihood results. Then conditioning on value of the unreliable estimate already in place in the portfolio, the density distribution obtained can be used to update the output of the “wrong” model and assess the impact in further calculations. This approach bridges the practitioners’ initial expectations with the model performance and provides an intuitive quantitative assessment for the impact in the follow-up calculations which are largely affected by the unreliable estimate. The presented approach is the first in literature to raise the concern of uncertain impact caused by “wrong” models and propose a solution. The pioneer demonstration using uncertainty in the loss given default (LGD) models as an example and assessing the impact on the then calculated regulatory capital provides a timely assessment tool for model risk management in the current banking industry. Note that the abuse of the word wrong in quotation marks is an exaggeration of the uncertainty involved, in practice, impact analysis could be requested at any level of uncertainty.