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Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities

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  • RÜDIGER FREY

    (Department of Mathematics, University of Leipzig, 04009 Leipzig, Germany)

  • JOCHEN BACKHAUS

    (Department of Mathematics, University of Leipzig, 04009 Leipzig, Germany)

Abstract

We consider reduced-form models for portfolio credit risk with interacting default intensities. In this class of models default intensities are modeled as functions of time and of the default state of the entire portfolio, so that phenomena such as default contagion or counterparty risk can be modeled explicitly. In the present paper this class of models is analyzed by Markov process techniques. We study in detail the pricing and the hedging of portfolio-related credit derivatives such as basket default swaps and collaterized debt obligations (CDOs) and discuss the calibration to market data.

Suggested Citation

  • Rüdiger Frey & Jochen Backhaus, 2008. "Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:06:n:s0219024908004956
    DOI: 10.1142/S0219024908004956
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    References listed on IDEAS

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    1. Herbertsson, Alexander, 2007. "Pricing Synthetic CDO Tranches in a Model with Default Contagion Using the Matrix-Analytic Approach," Working Papers in Economics 270, University of Gothenburg, Department of Economics.
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    Cited by:

    1. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2020. "Robust XVA," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 738-781, July.
    2. S. Heise & R. Kühn, 2012. "Derivatives and credit contagion in interconnected networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(4), pages 1-19, April.
    3. Pagès, Henri, 2013. "Bank monitoring incentives and optimal ABS," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 30-54.
    4. Nneka Umeorah & Phillip Mashele & Matthias Ehrhardt, 2021. "Pricing basket default swaps using quasi-analytic techniques," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 241-267, June.
    5. Agostino Capponi & Lijun Bo, 2016. "Robust Optimization of Credit Portfolios," Papers 1603.08169, arXiv.org.
    6. Lijun Bo & Huafu Liao & Yongjin Wang, 2018. "Optimal Credit Investment and Risk Control for an Insurer with Regime-Switching," Papers 1807.05513, arXiv.org.
    7. Wenqiong, Liu & Li, Shenghong, 2016. "Hedging default risks of CDO tranches in non-homogeneous Markovian contagion models," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 279-291.
    8. Wen-Qiong Liu & Wen-Li Huang, 2019. "Hedging Of Synthetic Cdo Tranches With Spread And Default Risk Based On A Combined Forecasting Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-17, March.
    9. Frey, Rüdiger & Backhaus, Jochen, 2010. "Dynamic hedging of synthetic CDO tranches with spread risk and default contagion," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 710-724, April.
    10. Areski Cousin & Diana Dorobantu & Didier Rullière, 2013. "An extension of Davis and Lo's contagion model," Quantitative Finance, Taylor & Francis Journals, vol. 13(3), pages 407-420, February.
    11. Bäuerle Nicole & Schmock Uwe, 2012. "Dependence properties of dynamic credit risk models," Statistics & Risk Modeling, De Gruyter, vol. 29(3), pages 243-268, August.
    12. Henri Pages & Dylan Possamaï, 2014. "A mathematical treatment of bank monitoring incentives," Finance and Stochastics, Springer, vol. 18(1), pages 39-73, January.
    13. Areski Cousin & Stéphane Crépey & Yu Kan, 2012. "Delta-hedging correlation risk?," Review of Derivatives Research, Springer, vol. 15(1), pages 25-56, April.
    14. Lijun Bo & Huafu Liao & Xiang Yu, 2017. "Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching," Papers 1712.05676, arXiv.org, revised Oct 2018.
    15. Delia Coculescu & Gabriele Visentin, 2017. "A default system with overspilling contagion," Papers 1709.09255, arXiv.org, revised May 2023.
    16. Takada, Hideyuki & Sumita, Ushio, 2011. "Credit risk model with contagious default dependencies affected by macro-economic condition," European Journal of Operational Research, Elsevier, vol. 214(2), pages 365-379, October.
    17. Herbertsson, Alexander, 2023. "Risk management of stock portfolios with jumps at exogenous default events," Working Papers in Economics 836, University of Gothenburg, Department of Economics.
    18. Dai Pra, Paolo & Tolotti, Marco, 2009. "Heterogeneous credit portfolios and the dynamics of the aggregate losses," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2913-2944, September.
    19. Chen, Tingqiang & Wang, Jiepeng & Liu, Haifei & He, Yuanping, 2019. "Contagion model on counterparty credit risk in the CRT market by considering the heterogeneity of counterparties and preferential-random mixing attachment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 458-480.
    20. Tao Peng, 2010. "Portfolio Credit Risk Modelling and CDO Pricing - Analytics and Implied Trees from CDO Tranches," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2010.
    21. Pagès, H., 2009. "Bank incentives and optimal CDOs," Working papers 253, Banque de France.
    22. Jean-David Fermanian & Olivier Vigneron, 2012. "On break-even correlation: the way to price structured credit derivatives by replication," Papers 1204.2251, arXiv.org.
    23. Emilio Barucci & Marco Tolotti, 2009. "The dynamics of social interaction with agents’ heterogeneity," Working Papers 189, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    24. Rainer Jobst & Daniel Rösch & Harald Scheule & Martin Schmelzle, 2015. "A Simple Econometric Approach for Modeling Stress Event Intensities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(4), pages 300-320, April.
    25. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2018. "Robust XVA," Papers 1808.04908, arXiv.org, revised Feb 2020.

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