Bayesian Analysis of Uncertainty in Internal Rating Based PD Models

Abstract

The Internal Rating Based (IRB) approach is a regulatory approach that allows the banks to estimate the Probability of Default (PD) using own model. The estimated PD is then used in the calculation of the regulatory capital, thus the bank’s capital is affected by any uncertainties found in the underlying PD model. In this paper, we highlight 3 areas where uncertainty in IRB PD modelling: observed Default Rates (DR), impact of overrides and multi-period default experience. Section 1 review the common practice of how the regulatory PD models are used in the finance industry. Section 2 and 3 introduce the Bayesian Framework and establish the Master Scale based initial expectation. We then conduct the observed data analysis for both default rate and override discussions in Section 4. Section 5 extend the analysis with the post-observation update. Section 6 present the proposed measures for each of the 3 types of uncertainties. The proposed framework is the first attempt in quantitatively assessing the uncertainty in the IRB PD models, moreover, this framework helps to combine initial understanding of the bank’s internal default experience with the latest observations so that the latest expectation is quantitatively measured and real data based.

Keywords: Probability of Default, PD Master Scale, Internal Rating Based PD, PD Master Scale, Bayesian PD Estimate, Observed Default Rate, PD Override analysis, Multi-period Long-term Default.