Approximate Default Probabilities of a Holding Company, with Complete and Partial Information
Forthcoming in Journal of Computational and Applied Mathematics
25 Pages Posted: 3 Feb 2013 Last revised: 26 Oct 2014
Date Written: December 18, 2012
Abstract
This paper studies the valuation of credit risk for firms that own several subsidiaries or business lines. We provide simple analytical approximating expressions for probabilities of default, and for equity-debt market values, both in the case when the information is available in continuous time as well as in the case that it is not instantaneously available. The total firm's asset value being modeled as a sum of lognormal random variables, we use convex upper and lower approximations to infer these analytical approximating expressions. We extend the model to firms financed by multiple stochastic liabilities and conclude by numerical illustrations.
Keywords: default risk, structural model, incomplete information, convex ordering, comonotonicity
JEL Classification: C02
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