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

24 Pages Posted: 15 Oct 2012 Last revised: 7 Apr 2013

See all articles by Tomasz R. Bielecki

Tomasz R. Bielecki

Illinois Institute of Technology

Areski Cousin

Université Lyon 1 - ISFA

Stéphane Crépey

Université d'Évry - Equipe d'Analyse et Probabilites

Alexander Herbertsson

University of Gothenburg - Department of Economics/Centre for Finance

Date Written: March 8, 2013

Abstract

In "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model", 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 "A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part I: Markov Copula Perspective" and "A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part II: Common-Shock Interpretation, Calibration and Hedging issues" 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 "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model" while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives ("Valuation and Hedging of CDS Counterparty Exposure in a Markov Copula Model", "CVA computation for counterparty risk assessment in credit portfolios", "Counterparty Risk Modeling - Collateralization, Funding and Hedging") , 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 "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model", "A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part I: Markov Copula Perspective" and "A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part II: Common-Shock Interpretation, Calibration and Hedging issues".

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

Suggested Citation

Bielecki, Tomasz R. and Cousin, Areski and Crépey, Stéphane and Herbertsson, Alexander, A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries (March 8, 2013). Available at SSRN: https://ssrn.com/abstract=2159279 or http://dx.doi.org/10.2139/ssrn.2159279

Tomasz R. Bielecki

Illinois Institute of Technology ( email )

Department of Applied Mathematics
10 W. 32nd Street
Chicago, IL 60616
United States
312 567 3185 (Phone)
312 567 3135 (Fax)

Areski Cousin

Université Lyon 1 - ISFA ( email )

50 avenue Tony Garnier
69007, Lyon
France

Stéphane Crépey

Université d'Évry - Equipe d'Analyse et Probabilites ( email )

Boulevard des Coquibus
F-91025 Evry Cedex
France

Alexander Herbertsson (Contact Author)

University of Gothenburg - Department of Economics/Centre for Finance ( email )

Box 640
Vasagatan 1, E-building, floor 5 & 6
Göteborg, 40530
Sweden

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