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Markov Chain Models of Portfolio Credit Risk

by Tomasz R. Bielecki of the Illinois Institute of Technology,
Stéphane Crépey of the Université d'Évry Val d'Essonne, and
Alexander Herbertsson of the University of Gothenburg

November 23, 2009

Abstract: In this paper, we present a selection of methods and results regarding various applications of the theory of continuous time Markov chains to valuation of credit derivatives. We present both theoretical and numerical aspects of the Markovian methodology.

After a review of some basic notions and results from the theory of continuous-time Markov chains in section 2, sections 3 to 5 are devoted to the study of a few specific Markovian models of portfolio credit risk.

Keywords: continuous time Markov chains, phase-type distributions, calibration.

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