Smoothing algorithms by constrained maximum likelihood: methodologies and implementations for Comprehensive Capital Analysis and Review stress testing and International Financial Reporting Standard 9 expected credit loss estimation

Bill Huajian Yang

Journal of Risk Model Validation

Abstract: In the process of loan pricing, stress testing, capital allocation, modeling of probability of default (PD) term structure and International Financial Reporting Standard 9 expected credit loss estimation, it is widely expected that higher risk grades carry higher default risks, and that an entity is more likely to migrate to a closer nondefault rating than a more distant nondefault rating. In practice, sample estimates for the rating-level ;default rate or rating migration probability do not always respect this monotonicity rule, and hence the need for smoothing approaches arises. Regression and interpolation ;techniques are widely ;used for this purpose. A common issue with these, however, is that the risk scale for the estimates is not fully justified, leading to a possible bias in credit loss estimates. In this paper, we propose smoothing algorithms for rating-level PD and rating migration probability. The smoothed estimates obtained by these approaches are optimal ;in the sense of constrained maximum likelihood, with a fair risk scale determined by constrained maximum likelihood, leading to more robust credit loss estimation. The proposed algorithms can be easily implemented by a modeler using, for example, the SAS procedure PROC NLMIXED. ;The approaches proposed in this paper will provide an effective and useful smoothing tool for practitioners in the field of risk modeling.

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