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BSDEs of counterparty risk

Author

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  • Crépey, Stéphane
  • Song, Shiqi

Abstract

We study a BSDE with random terminal time that appears in the modeling of counterparty risk in finance. We model the terminal time as an invariant time, i.e. a time such that local martingales with respect to a reduced filtration and a possibly changed probability measure, once stopped right before that time, stay local martingales with respect to the original model filtration and probability measure. Using an Azéma supermartingale characterization of invariant times, we establish the equivalence between the original and a reduced BSDE.

Suggested Citation

  • Crépey, Stéphane & Song, Shiqi, 2015. "BSDEs of counterparty risk," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3023-3052.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:3023-3052
    DOI: 10.1016/j.spa.2015.02.010
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/5717 is not listed on IDEAS
    2. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
    3. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
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    Citations

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    Cited by:

    1. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2016. "Arbitrage-Free XVA," Papers 1608.02690, arXiv.org.
    2. Han, Xingyu, 2018. "Pricing and hedging vulnerable option with funding costs and collateral," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 103-115.
    3. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    4. Lokman A Abbas-Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA Regressions With Oversimulated Defaults," Post-Print hal-03910149, HAL.
    5. Anna Aksamit & Libo Li & Marek Rutkowski, 2021. "Generalized BSDEs with random time horizon in a progressively enlarged filtration," Papers 2105.06654, arXiv.org.
    6. Junbeom Lee & Chao Zhou, 2021. "Binary funding impacts in derivative valuation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 242-278, January.
    7. Lokman Abbas-Turki & St'ephane Cr'epey & Botao Li & Bouazza Saadeddine, 2024. "An Explicit Scheme for Pathwise XVA Computations," Papers 2401.13314, arXiv.org.
    8. Weijie Pang & Stephan Sturm, 2020. "XVA Valuation under Market Illiquidity," Papers 2011.03543, arXiv.org.
    9. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2018. "Robust XVA," Papers 1808.04908, arXiv.org, revised Feb 2020.
    10. Damiano Brigo & Federico Graceffa & Alexander Kalinin, 2021. "Mild to classical solutions for XVA equations under stochastic volatility," Papers 2112.11808, arXiv.org.
    11. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2020. "Robust XVA," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 738-781, July.
    12. St'ephane Cr'epey & Shiqi Song, 2017. "Invariance times," Papers 1702.01045, arXiv.org.
    13. Lokman A. Abbas‐Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA regressions with oversimulated defaults," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 274-307, April.
    14. Stéphane Crépey & Shiqi Song, 2017. "Invariance Times ," Working Papers hal-01455414, HAL.
    15. Lokman Abbas-Turki & St'ephane Cr'epey & Bouazza Saadeddine, 2022. "Pathwise CVA Regressions With Oversimulated Defaults," Papers 2211.17005, arXiv.org.

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