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Asymmetric and Imperfect Collateralization, Derivative Pricing, and CVA

Author

Listed:
  • Masaaki Fujii

    (Graduate School of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party credit risk. By introducing the collateral coverage ratio, our framework can handle these issues in an unified manner. Although the resultant pricing formula becomes non-linear FBSDE and cannot be solve exactly, the fist order approximation is provided using Gateaux derivative. We have shown that it allows us to decompose the price of generic contract into three parts: market benchmark, bilateral credit value adjustment (CVA), and the collateral cost adjustment (CCA) independent from the credit risk. We have studied each term closely, and demonstrated the significant impact of asymmetric collateralization through CCA using the numerical examples.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2010. "Asymmetric and Imperfect Collateralization, Derivative Pricing, and CVA," CIRJE F-Series CIRJE-F-781, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2010cf781
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    References listed on IDEAS

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    1. Michael Johannes & Suresh Sundaresan, 2007. "The Impact of Collateralization on Swap Rates," Journal of Finance, American Finance Association, vol. 62(1), pages 383-410, February.
    2. Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," CIRJE F-Series CIRJE-F-802, CIRJE, Faculty of Economics, University of Tokyo.
    3. Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," CARF F-Series CARF-F-248, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    5. Masaaki Fujii & Akihiko Takahashi, 2010. "Modeling of Interest Rate Term Structures under Collateralization and its Implications," CIRJE F-Series CIRJE-F-762, CIRJE, Faculty of Economics, University of Tokyo.
    6. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Note on Construction of Multiple Swap Curves with and without Collateral," CIRJE F-Series CIRJE-F-630, CIRJE, Faculty of Economics, University of Tokyo.
    7. Feldhütter, Peter & Lando, David, 2008. "Decomposing swap spreads," Journal of Financial Economics, Elsevier, vol. 88(2), pages 375-405, May.
    8. Masaaki Fujii & Akihiko Takahashi, 2010. "Modeling of Interest Rate Term Structures under Collateralization and its Implications," CARF F-Series CARF-F-230, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2010.
    9. Duffie, Darrell & Huang, Ming, 1996. "Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
    10. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CIRJE F-Series CIRJE-F-698, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

    1. Masaaki Fujii & Akihiko Takahashi, 2011. "Collateralized CDS and Default Dependence -Implications for the Central Clearing-," CIRJE F-Series CIRJE-F-799, CIRJE, Faculty of Economics, University of Tokyo.
    2. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," CARF F-Series CARF-F-270, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2012.
    3. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CARF F-Series CARF-F-196, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Apr 2011.
    4. 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.
    5. Masaaki Fujii, Akihiko Takahashi, 2011. "Clean Valuation Framework for the USD Silo -An implication for the forthcoming Standard Credit Support Annex (SCSA)-," CARF F-Series CARF-F-260, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Yusuke Morimoto, 2015. "Application of Stochastic Mesh Method to Efficient Approximation of CVA," Papers 1510.04588, arXiv.org.
    7. Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," CIRJE F-Series CIRJE-F-802, CIRJE, Faculty of Economics, University of Tokyo.
    8. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," Papers 1202.0608, arXiv.org, revised Sep 2012.
    9. Akihiko Takahashi & Toshihiro Yamada, 2012. "An Asymptotic Expansion for Forward-Backward SDEs: A Malliavin Calculus Approach," CARF F-Series CARF-F-296, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2013.
    10. Sakurai, Yuji & Uchida, Yoshihiko, 2014. "Rehypothecation dilemma: Impact of collateral rehypothecation on derivative prices under bilateral counterparty credit risk," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 361-373.
    11. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CIRJE F-Series CIRJE-F-698, CIRJE, Faculty of Economics, University of Tokyo.
    12. Tomasz R. Bielecki & Marek Rutkowski, 2013. "Valuation and hedging of OTC contracts with funding costs, collateralization and counterparty credit risk: Part 1," Papers 1306.4733, arXiv.org, revised Jun 2013.
    13. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 1-24.
    14. Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," CARF F-Series CARF-F-248, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    15. Masaaki Fujii & Akihiko Takahashi, 2011. "Collateralized CDS and Default Dependence -Implications for the Central Clearing-," CARF F-Series CARF-F-246, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. Masaaki Fujii & Akihiko Takahashi, 2011. "Clean Valuation Framework for the USD Silo -An implication for the forthcoming Standard Credit Support Annex (SCSA)-," CIRJE F-Series CIRJE-F-829, CIRJE, Faculty of Economics, University of Tokyo.
    17. Masaaki Fujii & Akihiko Takahashi, 2011. "Clean Valuation Framework for the USD Silo," Papers 1112.1763, arXiv.org.
    18. Masaaki Fujii & Akihiko Takahashi, 2012. "Collateralized CDS and Default Dependence -Implications for the Central Clearing," CARF F-Series CARF-F-281, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    19. Akihiko Takahashi & Toshihiro Yamada, 2012. "An Asymptotic Expansion for Forward-Backward SDEs; A Malliavin Calculus Aproach," CIRJE F-Series CIRJE-F-865, CIRJE, Faculty of Economics, University of Tokyo.
    20. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," CIRJE F-Series CIRJE-F-840, CIRJE, Faculty of Economics, University of Tokyo.

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