Smoothing Algorithms by Constrained Maximum Likelihood

Bill Huajian Yang

MPRA Paper from University Library of Munich, Germany

Abstract: In the process of loan pricing, stress testing, capital allocation, modeling of PD term structure, and IFRS9 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 non-default rating than a farther away non-default rating. In practice, sample estimates for rating level default rate or rating migration probability do not always respect this monotonicity rule, and hence the need for smoothing approaches. Regression and interpolation techniques are widely used for this purpose. A common issue with these approaches 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 modeller 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.

Keywords: Credit loss estimation; risk scale; constrained maximum likelihood; PD term structure; rating migration probability (search for similar items in EconPapers)
JEL-codes: C1 C13 C18 C5 C51 C52 C53 C54 C61 C63 E5 G31 G38 O32 O33 O38 (search for similar items in EconPapers)
Date: 2017-06
New Economics Papers: this item is included in nep-ecm, nep-mac and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/79911/1/MPRA_paper_79911.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:79911

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().