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Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model

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 8, 2012

Abstract: We consider a bottom-up Markovian copula model of portfolio credit risk where dependence among credit names mainly stems from the possibility of simultaneous defaults.  Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In addition, the model admits a common shocks interpretation, which is a very important feature as, thanks to it, efficient convolution recursion procedures are available for pricing and hedging CDO tranches, conditionally on any given state of the underlying multivariate Markov process. As a result this model allows us to dynamically hedge CDO tranches using single-name CDSs in a theoretically sound and practically convenient way. To illustrate this we calibrate the model against market data on CDO tranches and the underlying single-name CDSs. We then study the loss distributions as well as the min-variance hedging strategies in the calibrated portfolios.

Keywords: Portfolio Credit Risk,  Basket Credit Derivatives,  Markov Copula Model, Common Shocks, Dynamic Min-Variance Hedging.

Previously titled: Dynamic Modeling of Portfolio Credit Risk with Common Shocks

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