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Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA


  • Masaaki Fujii

    (Faculty of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)


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 as well as the associated CVA. We have presented approximate expressions for various cases using Gateaux derivative which allow straightforward numerical analysis. Numerical examples for CCS (cross currency swap) and IRS (interest rate swap) with asymmetric collateralization were also provided. They clearly show the practical relevance of sophisticated collateral management for financial firms. The valuation and the associated issue of collateral cost under the one-way CSA (or unilateral collateralization), which is common when SSA (sovereign, supranational and agency) entities are involved, have been also studied. We have also discussed some generic implications of asymmetric collateralization for netting and resolution of information.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi, 2010. "Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA," CARF F-Series CARF-F-240, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Mar 2011.
  • Handle: RePEc:cfi:fseres:cf240

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
    4. Feldh├╝tter, Peter & Lando, David, 2008. "Decomposing swap spreads," Journal of Financial Economics, Elsevier, vol. 88(2), pages 375-405, May.
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    Cited by:

    1. Giovanni Mottola, 2014. "A stochastic switching control model arising in general OTC contracts with contingent CSA in presence of CVA, collateral and funding," Papers 1412.1469,
    2. repec:wsi:ijtafx:v:16:y:2013:i:02:n:s0219024913500064 is not listed on IDEAS

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