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

Applied Stochastic Models in Business and Industry, Vol. 20, No. 2, pp. 155-170, 2004

Cass Business School Research Paper

Posted: 8 Apr 2005

See all articles by Ashay Kadam

Ashay Kadam

IIM Udaipur

Halina Frydman

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

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Abstract

The usual tool for modeling bond ratings migration is a discrete, time-homogeneuous 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 by the 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-nonhomogeneuous 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, Maximum Likelihood Estimation

JEL Classification: C13, G33

Suggested Citation

Kadam, Ashay and Frydman, Halina, Estimation in the Continuous Time Mover-Stayer Model with an Application to Bond Ratings Migration. Applied Stochastic Models in Business and Industry, Vol. 20, No. 2, pp. 155-170, 2004; Cass Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=684101

Ashay Kadam

IIM Udaipur ( email )

Mohanlal Sukhadia University Campus
Udaipur, Rajasthan 313001
India

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)

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