On the Equivalence of the KMV and Maximum Likelihood Methods for Structural Credit Risk Models

by Jin-Chuan Duan of the University of Toronto,
Geneviève Gauthier of HEC Montréal, and
Jean-Guy Simonato of HEC Montréal

June 15, 2005

Abstract: Moody’s KMV method is a popular commercial implementation of the structural credit risk model pioneered by Merton (1974). Among the key features of their implementation procedure is an algorithm for estimating the unobserved asset value and the unknown parameters. This estimation method has found its way to the recent academic literature, but has not yet been formally analyzed in terms of its statistical properties. This paper fills this gap and shows that, in the context of Merton’s model, the KMV estimates are identical to maximum likelihood estimates (MLE) developed in Duan Duan (1994). Unlike the MLE method, however, the KMV algorithm is silent about the distributional properties of the estimates and thus ill-suited for statistical inference. The KMV algorithm also cannot generate estimates for capital-structure specific parameters. In contrast, the MLE approach is flexible and can be readily applied to different structural credit risk models.

JEL Classification: C22, G13.

Keywords: Credit risk, transformed data, maximum likelihood, financial distress, EM algorithm.

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