Bayesian Inference for Issuer Heterogeneity in Credit Ratings Migration

26 Pages Posted: 15 Jan 2008

See all articles by Ashay Kadam

Ashay Kadam

IIM Udaipur

Peter Lenk

University of Michigan; University of Michigan, Stephen M. Ross School of Business


Rating transition matrices for corporate bond issuers are often based on fitting a discrete time Markov chain model to homogeneous cohorts. Literature has documented that rating migration matrices can differ considerably depending on the characteristics of the issuers in the pool used for estimation. However, it is also well known in literature that a continuous time Markov chain gives statistically superior estimates of the rating migration process. It remains to verify and quantify the issuer heterogeneity in rating migration behavior using a continuous time Markov chain. We fill this gap in literature. We provide Bayesian estimates to mitigate the problem of data sparsity. Default data, especially when narrowing down to issuers with specific characteristics, can be highly sparse. Using classical estimation tools in such a situation can result in large estimation errors. Hence we adopt Bayesian estimation techniques. We apply them to the Moodys corporate bond default database. Our results indicate strong country and industry effects on the determination of rating migration behavior. Using the CreditRisk+ framework, and a sample credit portfolio, we show that ignoring issuer heterogeneity can give erroneous estimates of Value-at-Risk and a misleading picture of the risk capital. This insight is consistent with some recent findings in literature. Therefore, given the upcoming Basel II implementation, understanding issuer heterogeneity has important policy implications.

Keywords: Credit risk, Risk Capital, Markov Chains, Bayesian Inference, Heterogeneity

JEL Classification: C11, C13, C41, G12

Suggested Citation

Kadam, Ashay and Lenk, Peter and Lenk, Peter, Bayesian Inference for Issuer Heterogeneity in Credit Ratings Migration. Journal of Banking and Finance, Forthcoming, Available at SSRN:

Ashay Kadam (Contact Author)

IIM Udaipur ( email )

Mohanlal Sukhadia University Campus
Udaipur, Rajasthan 313001

Peter Lenk

University of Michigan ( email )

701 Tappan St
Ann Arbor, MI 48109-1234
United States
+1 734 936-2619 (Phone)


University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

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