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Up and down credit risk

Author

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  • Tomasz Bielecki
  • Stephane Crepey
  • Monique Jeanblanc

Abstract

This paper discusses the main modeling approaches that have been developed for handling portfolio credit derivatives, with a focus on the question of hedging. In particular, the so-called top, top down and bottom up approaches are considered. We give some mathematical insights regarding the fact that information, namely the choice of a relevant model filtration, is the major modeling issue. In this regard, we examine the notion of thinning that was recently advocated for the purpose of hedging a multi-name derivative by single-name derivatives. We then illustrate by means of numerical simulations (semi-static hedging experiments) why and when the portfolio loss process may not be a 'sufficient statistic' for the purpose of valuation and hedging of portfolio credit risk.

Suggested Citation

  • Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc, 2010. "Up and down credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1137-1151.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:10:p:1137-1151
    DOI: 10.1080/14697680903382776
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    Citations

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    Cited by:

    1. Xin Gao & Binlin Wu & Tobias Schäfer, 2017. "Introducing an analytical solution and an improved one-factor gaussian copula model for the pricing of heterogeneous CDOs," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-17, June.
    2. Tomasz R. Bielecki & Areski Cousin & Stéphane Crépey & Alexander Herbertsson, 2014. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 90-102, April.
    3. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2017. "Dynamics of multivariate default system in random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3943-3965.
    4. Christian Koziol & Philipp Koziol & Thomas Schön, 2015. "Do correlated defaults matter for CDS premia? An empirical analysis," Review of Derivatives Research, Springer, vol. 18(3), pages 191-224, October.
    5. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2013. "Density approach in modelling multi-defaults," Working Papers hal-00870492, HAL.
    6. Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Reduced-form framework for multiple ordered default times under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 1-43.
    7. Zehra Eksi & Damir Filipovi'c, 2020. "Affine Pricing and Hedging of Collateralized Debt Obligations," Papers 2011.10101, arXiv.org.
    8. Cantia, Catalin & Tunaru, Radu, 2017. "A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 21-35.
    9. Rama Cont & Yu Hang Kan, 2011. "Dynamic hedging of portfolio credit derivatives," Post-Print hal-00578008, HAL.

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