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A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries

by Tomasz R. Bielecki of Illinois Institute of Technology,
Areski Cousin of Université Lyon 1, LSAF,
Stéphane Crépey of Université d'Evry Val d'Essonne, and
Alexander Herbertsson of University of Gothenburg

August 26, 2013

Abstract: In [5], the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developped in [6] and [7] where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we show how to incorporate stochastic default intensities and random recoveries in the bottom-up modeling framework of [5] while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives [10, 3, 2], as CVA is sensitive to the stochastic nature of credit spreads and random recoveries allow to achieve satisfactory calibration even for "badly behaved" data sets. This paper is thus a complement to [5], [6] and [7].

Keywords: Portfolio credit risk, Markov copula model, Common shocks, Stochastic spreads, Random recoveries.

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