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Counterparty risk and funding: immersion and beyond

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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.

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  1. Not written as not used in the paper.

References

  1. Albanese, C., Caenazzo, S., Crépey, S.: Capital valuation adjustment and funding valuation adjustment (2015). Preprint, available online at arXiv:1603.03012

  2. Armenti, Y., Crépey, S.: Central clearing valuation adjustment (2015). Preprint, available online at arXiv:1506.08595v2

  3. Bichuch, M., Capponi, A., Sturm, S.: Arbitrage-free pricing of XVA—Part I: framework and explicit examples (2015). Preprint, available online at arXiv:1501.05893

  4. Bielecki, T.R., Cousin, A., Crépey, S., Herbertsson, A.: Dynamic hedging of portfolio credit risk in a Markov copula model. J. Optim. Theory Appl. 161, 90–102 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bielecki, T.R., Jeanblanc, M., Rutkowski, M.: Credit Risk Modeling. Osaka University CSFI Lecture Notes Series, vol. 2. Osaka University Press, Osaka (2009)

    MATH  Google Scholar 

  6. Bielecki, T.R., Rutkowski, M.: Valuation and hedging of contracts with funding costs and collateralization. SIAM J. Financ. Math. 6, 594–655 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bo, L., Capponi, A.: Counterparty risk for CDS: default clustering effects. J. Bank. Finance 52, 29–42 (2015)

    Article  Google Scholar 

  8. Brigo, D., Pallavicini, A.: Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks. J. Financ. Eng. 1, 1–60 (2014)

    Google Scholar 

  9. Crépey, S.: Financial Modeling: A Backward Stochastic Differential Equations Perspective. Springer, Berlin (2013)

    Book  MATH  Google Scholar 

  10. Crépey, S.: Bilateral counterparty risk under funding constraints. Part II: CVA. Math. Finance 25, 23–50 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Crépey, S., Bielecki, T.R., Brigo, D.: Counterparty Risk and Funding: A Tale of Two Puzzles. Chapman & Hall/CRC Financial Mathematics Series (2014)

    MATH  Google Scholar 

  12. Crépey, S., Gerboud, R., Grbac, Z., Ngor, N.: Counterparty risk and funding: the four wings of the TVA. Int. J. Theor. Appl. Finance 16, 1350006, 31 pp. (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Crépey, S., Song, S.: BSDEs of counterparty risk. Stoch. Process. Appl. 125, 3023–3052 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Crépey, S., Song, S.: (2015). Invariance times. Preprint, available online at https://math.maths.univ-evry.fr/crepey

  15. Cvitanić, J., Karatzas, I.: Hedging contingent claims with constrained portfolios. Ann. Appl. Probab. 3, 652–681 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. El Karoui, N., Peng, S., Quenez, M.-C.: Backward stochastic differential equations in finance. Math. Finance 7, 1–71 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fujii, M., Takahashi, A.: Analytical approximation for non-linear FBSDEs with perturbation scheme. Int. J. Theor. Appl. Finance 15(5), 1250034, 24 pp. (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fujii, M., Takahashi, A.: Perturbative expansion technique for non-linear FBSDEs with interacting particle method. Asia-Pac. Financ. Mark. 22, 283–304 (2015)

    Article  Google Scholar 

  19. Gobet, E., Pagliarani, S.: Analytical approximations of BSDEs with nonsmooth driver. SIAM J. Financ. Math. 6, 919–958 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  20. He, S.-W., Wang, J.-G., Yan, J.-A.: Semimartingale Theory and Stochastic Calculus. CRC Press, Boca Raton (1992)

    MATH  Google Scholar 

  21. Hull, J., White, A.: The FVA debate. Risk Magazine, July, 83–85 (2012)

  22. Jeanblanc, M., Song, S.: Martingale representation theorem in progressively enlarged filtrations. Stoch. Process. Appl. 125, 4242–4271 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Korn, R.: Contingent claim valuation in a market with different interest rates. Math. Methods Oper. Res. 42, 255–274 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kruse, T., Popier, A.: BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. Stoch. Int. J. Probab. Stoch. Process. 88, 491–539 (2016)

    MathSciNet  MATH  Google Scholar 

  25. Song, S.: Local martingale deflators for asset processes stopped at a default time \(s^{\mathfrak{t}}\) or right before \(s^{\mathfrak{t}-}\). Working paper (2014). Available online at arXiv:1405.4474

  26. Song, S.: Optional splitting formula in a progressively enlarged filtration. ESAIM Probab. Stat. 18, 829–853 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  27. Takahashi, A., Yamada, T.: An asymptotic expansion of forward-backward SDEs with a perturbed driver. Int. J. Financ. Eng. 2, 1550020, 29 pp. (2015)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Modélisation d’Évry, 91037, Évry Cedex, France

    Stéphane Crépey & Shiqi Song

Authors
  1. Stéphane Crépey
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  2. Shiqi Song
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Corresponding author

Correspondence to Stéphane Crépey.

Additional information

This research benefited from the support of the “Chair Markets in Transition,” Fédération Bancaire Française, of the ANR project 11-LABX-0019 and of the EIF grant “Collateral management in centrally cleared trading”.

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Crépey, S., Song, S. Counterparty risk and funding: immersion and beyond. Finance Stoch 20, 901–930 (2016). https://doi.org/10.1007/s00780-016-0305-3

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  • DOI: https://doi.org/10.1007/s00780-016-0305-3

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