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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".

A Markov Copula Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries