Estimation in the Continuous Time Mover-Stayer Model with an Application to Bond Ratings Migration

24 Pages Posted: 3 Nov 2008

See all articles by Halina Frydman

Halina Frydman

New York University (NYU) - Department of Information, Operations, and Management Sciences

Ashay Kadam

IIM Udaipur

Multiple version iconThere are 2 versions of this paper

Date Written: December 2002

Abstract

The usual tool for modeling bond ratings migration is a discrete, time homogeneous Markov chain. Such model assumes that all bonds are homogeneous with respect to their movement behavior among rating categories and that the movement behavior does not change over time. However, among recognized sources of heterogeneity in ratings migration is age of a bond (time elapsed since issuance). It has been observed that young bonds have a lower propensity to change ratings, and thus to default, than more seasoned bonds. The aim of this paper is to introduce a continuous, time-nonhomogeneuous model for bond ratings migration, which also incorporates a simple form of population heterogeneity. The specific form of heterogeneity postulated bythe proposed model appears to be suitable for modeling the effect of age of a bond on its propensity to change ratings. This model, called a mover-stayer model, is an extension of a time-nonhomogeneous Markov chain. This paper derives the maximum likelihood estimators for the parameters of a continuous time mover-stayer model based on a sample of independent continuously monitored histories of the process, and develops the likelihood ratio test for discriminating between the Markov chain and the mover-stayer model. The methods are illustrated using a sample of rating histories of young corporate issuers. For this sample, the likelihood ratio test rejects a Markov chain in favor of a mover-stayer model. For young bonds with lowest rating the default probabilities predicted by the mover-stayer model are substantially lower than those predicted by the Markov chain.

Keywords: Ratings migration, mover-stayer model, Markov chain, estimation

Suggested Citation

Frydman, Halina and Kadam, Ashay, Estimation in the Continuous Time Mover-Stayer Model with an Application to Bond Ratings Migration (December 2002). Statistics Working Papers Series, Vol. , pp. -, 2002. Available at SSRN: https://ssrn.com/abstract=1293601

Halina Frydman (Contact Author)

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States
212-998-0453 (Phone)

Ashay Kadam

IIM Udaipur ( email )

Mohanlal Sukhadia University Campus
Udaipur, Rajasthan 313001
India

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