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Default probabilities of a holding company, with complete and partial information. † Donatien Hainaut Griselda Deelstra* January 20, 2014 † ESC Rennes Business School and CREST, France. * Department of Mathematics, Université libre de Bruxelles, Belgium . Email: donatien.hainaut@esc-rennes.fr; griselda.deelstra@ulb.ac.be 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 illustra- tions. Keywords. default risk, structural model, incomplete information, convex ordering, comono- tonicity. 1 Introduction. The treatment of default is a crucial issue in determining the value of corporate securities and the firm’s financing decisions. This task is particularly complex when the corporation is itself a group of subsidiaries that have dependent activities. Structural models such as developed by Merton (1974) and Black and Cox (1976) represent an elegant framework for the valuation of risky debts, when assets are mod

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