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Pricing And Hedging In A Dynamic Credit Model

In: Credit Correlation Life After Copulas

Author

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  • YOUSSEF ELOUERKHAOUI

    (CITIGROUP, Canada Square, Canary Wharf, London E14 5LB, United Kingdom)

Abstract

In this paper, we present a methodology for pricing and hedging portfolio credit derivatives in a dynamic credit model. Starting with a single-name Marshall–Olkin framework, we build a dynamic top-down version of the model, which is tractable and preserves the intuition of the original setting. In the first part of the paper, we derive analytically the Fourier transform of the loss variable and we study the skew dynamics implied by the model. In the second part, we develop a theory for dynamic hedging of portfolio credit derivatives. Since the market is incomplete, due to the residual correlation risk, perfect replication cannot be achieved. To find the hedging strategies, we use a quadratic risk minimization criterion.

Suggested Citation

  • Youssef Elouerkhaoui, 2007. "Pricing And Hedging In A Dynamic Credit Model," World Scientific Book Chapters, in: Alexander Lipton & Andrew Rennie (ed.), Credit Correlation Life After Copulas, chapter 6, pages 111-139, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812709509_0006
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    Citations

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    Cited by:

    1. Sabrina Mulinacci, 2022. "A Marshall-Olkin Type Multivariate Model with Underlying Dependent Shocks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2455-2484, December.
    2. Lokman A. Abbas-Turki & Stéphane Crépey & Babacar Diallo, 2018. "Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-40, September.
    3. Albanese Claudio & Armenti Yannick & Crépey Stéphane, 2020. "XVA metrics for CCP optimization," Statistics & Risk Modeling, De Gruyter, vol. 37(1-2), pages 25-53, January.
    4. Claudio Albanese & Stéphane Crépey & Rodney Hoskinson & Bouazza Saadeddine, 2021. "XVA analysis from the balance sheet," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 99-123, January.
    5. 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.
    6. David Barrera & Stéphane Crépey & Babacar Diallo & Gersende Fort & Emmanuel Gobet & Uladzislau Stazhynski, 2018. "Stochastic Approximation Schemes for Economic Capital and Risk Margin Computations," Working Papers hal-01710394, HAL.
    7. Bielecki, T.R. & Cousin, A. & Crépey, S. & Herbertsson, Alexander, 2012. "A Markov Copula Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries," Working Papers in Economics 545, University of Gothenburg, Department of Economics.
    8. Sabrina Mulinacci, 2017. "A systemic shock model for too big to fail financial institutions," Papers 1704.02160, arXiv.org, revised Apr 2017.
    9. Matthias Scherer & Henrik Sloot, 2019. "Exogenous shock models: analytical characterization and probabilistic construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 931-959, November.
    10. David Barrera & Stéphane Crépey & Babacar Diallo & Gersende Fort & Emmanuel Gobet & Uladzislau Stazhynski, 2019. "Stochastic Approximation Schemes for Economic Capital and Risk Margin Computations," Post-Print hal-01710394, HAL.
    11. Bielecki, Tomasz R. & Cousin, Areski & Crépey, Stéphane & Herbertsson, Alexander, 2011. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model (Previous title: Dynamic Modeling of Portfolio Credit Risk with Common Shocks)," Working Papers in Economics 502, University of Gothenburg, Department of Economics, revised 12 Oct 2012.

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