Affine Credit Risk Models under Incomplete Information

Rüdiger Frey, Cecilia Prosdocimi and Wolfgang J. Runggaldier
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Rüdiger Frey: Department of Mathematics, University of Leipzig 04081 Leipzig, Germany
Cecilia Prosdocimi: Dipartimento di Matematica Pura ed Aplicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy
Wolfgang J. Runggaldier: Dipartimento di Matematica Pura ed Aplicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy

Chapter 6 in Stochastic Processes and Applications to Mathematical Finance, 2007, pp 97-113 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe consider the problem of computing some basic quantities such as defaultable bond prices and survival probabilities in a credit risk model according to the intensity based approach. We let the default intensities depend on an external factor process that we assume is not observable. We use stochastic filtering to successively update its distribution on the basis of the observed default history. On one hand this allows us to capture aspects of default contagion (information-induced contagion). On the other hand it allows us to evaluate the above quantities also in our incomplete information context. We consider in particular affine credit risk models and show that in such models the nonlinear filter can be computed via a recursive procedure. This then leads to an explicit expression for the filter that depends on a finite number of sufficient statistics of the observed interarrival times for the defaults provided one chooses an initial distribution for the factor process that is of the Gamma type.

Keywords: Stochastic Calculus; Mathematical Finance; Insider Trading; Stochastic Control; Real Options; Filtering Model of Credit Risks; Stochastic Growth Models (search for similar items in EconPapers)
Date: 2007
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