IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v20y2016i4d10.1007_s00780-016-0305-3.html
   My bibliography  Save this article

Counterparty risk and funding: immersion and beyond

Author

Listed:
  • Stéphane Crépey

    (Laboratoire de Mathématiques et Modélisation d’Évry)

  • Shiqi Song

    (Laboratoire de Mathématiques et Modélisation d’Évry)

Abstract

In Crépey (Math. Finance 25:23–50, 2015), a basic reduced-form counterparty risk modelling approach was introduced under a standard immersion hypothesis between a reference filtration and the filtration progressively enlarged by the default times of the two parties. This basic setup, with a related continuity assumption on some of the data at the first default time of the two parties, is too restrictive for wrong-way and gap risk applications, such as counterparty risk on credit derivatives. This paper introduces an extension of the basic approach, implements it through marked default times and applies it to counterparty risk on credit derivatives.

Suggested Citation

  • Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:4:d:10.1007_s00780-016-0305-3
    DOI: 10.1007/s00780-016-0305-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-016-0305-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-016-0305-3?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Akihiko Takahashi & Toshihiro Yamada, 2015. "An Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver," CARF F-Series CARF-F-363, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Masaaki Fujii, Akihiko Takahashi, 2012. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," CARF F-Series CARF-F-269, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs," CARF F-Series CARF-F-372, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Masaaki Fujii & Akihiko Takahashi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 283-304, September.
    6. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs with Jumps," Papers 1510.03220, arXiv.org, revised Sep 2018.
    7. 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.
    8. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs with Jumps," CIRJE F-Series CIRJE-F-993, CIRJE, Faculty of Economics, University of Tokyo.
    9. Masaaki Fujii & Akihiko Takahshi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," CIRJE F-Series CIRJE-F-954, CIRJE, Faculty of Economics, University of Tokyo.
    10. Crépey, Stéphane & Song, Shiqi, 2015. "BSDEs of counterparty risk," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3023-3052.
    11. Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," Papers 1106.0123, arXiv.org, revised Jan 2012.
    12. Akihiko Takahashi & Toshihiro Yamada, 2015. "An asymptotic expansion of forward-backward SDEs with a perturbed driver," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-29.
    13. Masaaki Fujii & Akihiko Takahashi, 2012. "ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDEs WITH PERTURBATION SCHEME," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1-24.
    14. Bo, Lijun & Capponi, Agostino, 2015. "Counterparty risk for CDS: Default clustering effects," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 29-42.
    15. Akihiko Takahashi & Toshiaki Watanabe, 2015. "An Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver ," CIRJE F-Series CIRJE-F-976, CIRJE, Faculty of Economics, University of Tokyo.
    16. 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.
    17. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," CARF F-Series CARF-F-278, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2015.
    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. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," Papers 1710.07030, arXiv.org, revised Mar 2019.
    2. 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.
    3. Stéphane Crépey & Matthew F Dixon, 2020. "Gaussian process regression for derivative portfolio modeling and application to credit valuation adjustment computations," Post-Print hal-03910109, HAL.
    4. Frédéric Vrins, 2017. "Wrong-Way Risk Cva Models With Analytical Epe Profiles Under Gaussian Exposure Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-35, November.
    5. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    6. St'ephane Cr'epey & Shiqi Song, 2017. "Invariance times," Papers 1702.01045, arXiv.org.
    7. St'ephane Cr'epey & Shiqi Song, 2017. "Invariance properties in the dynamic gaussian copula model ," Papers 1702.03232, arXiv.org.
    8. St'ephane Cr'epey & Matthew Dixon, 2019. "Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations," Papers 1901.11081, arXiv.org, revised Oct 2019.
    9. 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.
    10. Marc Chataigner & Stéphane Crépey, 2019. "Credit Valuation Adjustment Compression by Genetic Optimization," Risks, MDPI, vol. 7(4), pages 1-21, September.
    11. Brigo, Damiano & Francischello, Marco & Pallavicini, Andrea, 2019. "Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement," European Journal of Operational Research, Elsevier, vol. 274(2), pages 788-805.
    12. 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.
    13. 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.
    14. Tomasz R. Bielecki & Igor Cialenco & Marek Rutkowski, 2017. "Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models," Papers 1701.08399, arXiv.org, revised Apr 2018.
    15. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2022. "Nonlinear Valuation with XVAs: Two Converging Approaches," Mathematics, MDPI, vol. 10(5), pages 1-31, March.
    16. Stéphane Crépey & Shiqi Song, 2017. "Invariance properties in the dynamic gaussian copula model ," Working Papers hal-01455424, HAL.
    17. 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.
    18. Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs," Papers 2212.12854, arXiv.org.
    19. Stéphane Crépey & Shiqi Song, 2017. "Invariance Times ," Working Papers hal-01455414, HAL.
    20. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2018. "Risk-neutral valuation under differential funding costs, defaults and collateralization," Papers 1802.10228, arXiv.org.
    21. Junbeom Lee & Chao Zhou, 2017. "Binary Funding Impacts in Derivative Valuation," Papers 1703.00259, arXiv.org, revised Aug 2020.
    22. Damiano Brigo & Federico Graceffa & Alexander Kalinin, 2021. "Mild to classical solutions for XVA equations under stochastic volatility," Papers 2112.11808, arXiv.org.
    23. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CIRJE F-Series CIRJE-F-1069, CIRJE, Faculty of Economics, University of Tokyo.
    24. Jun Sekine & Akihiro Tanaka, 2020. "Notes on Backward Stochastic Differential Equations for Computing XVA," Papers 2006.02173, arXiv.org.
    25. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CARF F-Series CARF-F-423, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    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. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    2. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CIRJE F-Series CIRJE-F-1069, CIRJE, Faculty of Economics, University of Tokyo.
    3. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions," CIRJE F-Series CIRJE-F-1016, CIRJE, Faculty of Economics, University of Tokyo.
    4. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions," Papers 1606.04285, arXiv.org, revised May 2018.
    5. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CARF F-Series CARF-F-423, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," Papers 1710.07030, arXiv.org, revised Mar 2019.
    7. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 391-408, September.
    8. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions(Revised version of CARF-F-387)," CARF F-Series CARF-F-398, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs with Jumps," Papers 1510.03220, arXiv.org, revised Sep 2018.
    10. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-456, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Stéphane Crépey & Shiqi Song, 2018. "Counterparty risk and funding: immersion and beyond," Working Papers hal-01764403, HAL.
    12. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions," CARF F-Series CARF-F-387, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    13. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs with Jumps," CIRJE F-Series CIRJE-F-993, CIRJE, Faculty of Economics, University of Tokyo.
    14. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs," CARF F-Series CARF-F-372, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    15. Masaaki Fujii & Akihiko Takahashi, 2018. "Asymptotic Expansion for Forward-Backward SDEs with JumpsAsymptotic Expansion for Forward-Backward SDEs with Jumps (Forthcoming in Stochastics) (Revised version of F-372)," CARF F-Series CARF-F-445, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. Fujii, Masaaki & Takahashi, Akihiko, 2018. "Quadratic–exponential growth BSDEs with jumps and their Malliavin’s differentiability," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2083-2130.
    17. Akihiko Takahashi & Toshihiro Yamada, 2016. "An Asymptotic Expansion for Forward–Backward SDEs: A Malliavin Calculus Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 337-373, December.
    18. Yoshifumi Tsuchida, 2023. "Control Variate Method for Deep BSDE Solver Using Weak Approximation," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 273-296, June.
    19. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," Papers 2101.09890, arXiv.org, revised Jan 2021.
    20. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A New Efficient Approximation Scheme for Solving High-Dimensional Semilinear PDEs: Control Variate Method for Deep BSDE Solver," CIRJE F-Series CIRJE-F-1159, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    Keywords

    Counterparty risk; Funding; BSDE; Reduced-form credit modelling; Immersion; Wrong-way risk; Gap risk; Collateral; Credit derivatives; Marked default times; Marshall–Olkin copula;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:spr:finsto:v:20:y:2016:i:4:d:10.1007_s00780-016-0305-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.