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

Journal article
Authors Tomasz R. Bielecki
Areski Cousin
Stéphane Crépey
Alexander Herbertsson
Published in Communications in Statistics - Theory and Methods
Volume 43
Issue 7
Pages 1362-1389
ISSN 0361-0926
Publication year 2014
Published at Department of Economics
Pages 1362-1389
Language en
Keywords Common shocks, Markov copula model, Portfolio credit risk, Random recoveries, Stochastic spreads
Subject categories Applied mathematics, Mathematical statistics, Economics and Business


In Bielecki et al. (2014a), 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 developed in Bielecki et al. (2014b,c) 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 Bielecki et al. (2014a) while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives (Assefa et al., 2011; Bielecki et al., 2012), 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 article is thus a complement to Bielecki et al. (2014a), Bielecki et al. (2014b) and Bielecki et al. (2014c).

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