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Collateralized CDS and Default Dependence -Implications for the Central Clearing

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  • Masaaki Fujii

    (Graduate School of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Graduate School of Economics, The University of Tokyo)

Abstract

In this paper, we have studied the pricing of a continuously collateralized CDS. We have made use of the "survival measure" to derive the pricing formula in a straightforward way. As a result, we have found that there exists irremovable trace of the counter party as well as the investor in the price of CDS through their default dependence even under the perfect collateralization, although the hazard rates of the two parties are totally absent from the pricing formula. As an important implication, we have also studied the situation where the investor enters an offsetting back-to-back trade with another counter party. We have provided simple numerical examples to demonstrate the change of a fair CDS premium according to the strength of default dependence among the relevant names, and then discussed its possible implications for the risk management of the central counter parties.

Suggested Citation

  • 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.
    • Handle: RePEc:cfi:fseres:cf281
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    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/293.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Price Impacts of Imperfect Collateralization," CIRJE F-Series CIRJE-F-947, CIRJE, Faculty of Economics, University of Tokyo.
    2. Akihiko Takahashi & Toshihiro Yamada, 2016. "An Asymptotic Expansion for Forward-Backward SDEs: A Malliavin Calculus Approach," CIRJE F-Series CIRJE-F-1009, CIRJE, Faculty of Economics, University of Tokyo.
    3. Akihiko Takahashi & Toshihiro Yamada, 2016. "An asymptotic expansion for forward-backward SDEs: a Malliavin calculus approach (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-394, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Bo, Lijun & Capponi, Agostino, 2015. "Counterparty risk for CDS: Default clustering effects," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 29-42.
    5. Kenichiro Shiraya & Akihiko Takahashi, 2015. "Price Impacts of Imperfect Collateralization (Revised version of CARF-F-355; Subsequently published in "International Journal of Financial Engineering")," CARF F-Series CARF-F-375, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. 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.
    7. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Price Impacts of Imperfect Collateralization," CARF F-Series CARF-F-355, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2015.

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