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A Markov Copula 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'Évry Val d'Essonne, and
Alexander Herbertsson of University of Gothenburg

October 4, 2012

Abstract: In [4], the authors introduced a  Markov copula model of portfolio credit risk. This model solves the  top-down versus bottom-up puzzle in achieving efficient joint calibration to single-name CDS and to multi-name CDO tranches data. In [4], we studied a general model, that allows for stochastic default intensities and for random recoveries, and we conducted empirical study of our model using both deterministic and stochastic default intensities, as well as deterministic and random recoveries only. Since, in case of some "badly behaved'' data sets a satisfactory calibration accuracy can only be achieved through the use of random recoveries, and, since for important applications, such as CVA computations for credit derivatives, the use of stochastic intensities is advocated by practitioners, efficient implementation of our model that would account for these two issues is very important. However, the details behind the implementation of the loss distribution in the case with random recoveries were not provided in [4]. Neither were the details on the stochastic default intensities given there. This paper is thus a  complement to [4], with a focus on a detailed description of the methodology that we used so to implement these two model features: random recoveries and stochastic intensities.

Keywords: Portfolio Credit Risk,  Markov Copula Model, Common Shocks, Stochastic Spreads, Random Recoveries.

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