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Bivariate Semi-Markov Process for Counterparty Credit Risk

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  • Guglielmo D'Amico
  • Raimondo Manca
  • Giovanni Salvi

Abstract

We consider the problem of constructing an appropriate multivariate model for the study of the counterparty credit risk in credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However the markovian assumption may be inappropriate for the study of the dynamic of credit ratings which typically show non markovian like behaviour. In this paper we develop a semi-Markov approach to the study of the counterparty credit risk by defining a new multivariate semi-Markov chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap.

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  • Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2011. "Bivariate Semi-Markov Process for Counterparty Credit Risk," Papers 1112.0226, arXiv.org, revised Oct 2012.
    • Handle: RePEc:arx:papers:1112.0226
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    References listed on IDEAS

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    1. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2011. "Discrete Time Non-Homogeneous Semi-Markov Reliability Transition Credit Risk Models and the Default Distribution Functions," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 465-481, November.
    2. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2007. "Valuing credit default swap in a non-homogeneous semi-Markovian rating based model," Computational Economics, Springer;Society for Computational Economics, vol. 29(2), pages 119-138, March.
    3. Damiano Brigo & Agostino Capponi, 2008. "Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps," Papers 0812.3705, arXiv.org, revised Nov 2009.
    4. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2010. "Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 215-225, June.
    5. Guglielmo D'Amico & Jacques Janssen & Raimondo Manca, 2011. "A Non-Homogeneous Semi-Markov Reward Model For The Credit Spread Computation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 221-238.
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