IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i8p3023-3052.html

BSDEs of counterparty risk

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915000605
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.02.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/5717 is not listed on IDEAS
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Stéphane Crépey & Shiqi Song, 2014. "BSDEs of Counterparty Risk," Working Papers hal-01088941, HAL.
    3. Kreher, Dörte, 2017. "Change of measure up to a random time: Details," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1565-1598.
    4. Bao, Qunfang & Li, Shenghong & Liu, Guimei, 2010. "Survival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing," MPRA Paper 27698, University Library of Munich, Germany, revised 27 Dec 2010.
    5. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 31, July-Dece.
    6. Fisher, Travis & Pulido, Sergio & Ruf, Johannes, 2019. "Financial models with defaultable numéraires," LSE Research Online Documents on Economics 84973, London School of Economics and Political Science, LSE Library.
    7. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2016. "Arbitrage-Free XVA," Papers 1608.02690, arXiv.org.
    8. Han, Xingyu, 2018. "Pricing and hedging vulnerable option with funding costs and collateral," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 103-115.
    9. Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2015. "Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs," Papers 1506.00686, arXiv.org, revised Nov 2015.
    10. Herbertsson, Alexander, 2007. "Modelling Default Contagion Using Multivariate Phase-Type Distributions," Working Papers in Economics 271, University of Gothenburg, Department of Economics.
    11. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    12. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2007, January-A.
    13. repec:mth:ijafr8:v:8:y:2018:i:4:p:248-286 is not listed on IDEAS
    14. Claudio Albanese & Simone Caenazzo & Stéphane Crépey, 2016. "Capital Valuation Adjustment and Funding Valuation Adjustment," Working Papers hal-01285363, HAL.
    15. Umut c{C}etin, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Papers 1205.1154, arXiv.org.
    16. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2018. "Robust XVA," Papers 1808.04908, arXiv.org, revised Feb 2020.
    17. Ron Berndsen, 2021. "Fundamental questions on central counterparties: A review of the literature," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(12), pages 2009-2022, December.
    18. Travis Fisher & Sergio Pulido & Johannes Ruf, 2019. "Financial Models with Defaultable Numéraires," Post-Print hal-01240736, HAL.
    19. 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.
    20. James Wolter, 2015. "Asymptotics for Sieve Estimators of Hazard Rates: Estimating Hazard Functionals," Economics Series Working Papers 760, University of Oxford, Department of Economics.
    21. Muendler, Marc-Andreas, 2008. "Risk-neutral investors do not acquire information," Finance Research Letters, Elsevier, vol. 5(3), pages 156-161, September.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:3023-3052. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.