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Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA

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  • Masaaki Fujii
  • Akihiko Takahashi

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.

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  • Masaaki Fujii & Akihiko Takahashi, 2011. "Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA," Papers 1101.5849, arXiv.org, revised Dec 2011.
    • Handle: RePEc:arx:papers:1101.5849
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    Cited by:

    1. St'ephane Cr'epey & R'emi Gerboud & Zorana Grbac & Nathalie Ngor, 2012. "Counterparty Risk and Funding: The Four Wings of the TVA," Papers 1210.5046, arXiv.org.
    2. 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, arXiv.org.
    3. Stéphane Crépey & Rémi Gerboud & Zorana Grbac & Nathalie Ngor, 2013. "Counterparty Risk And Funding: The Four Wings Of The Tva," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-31.

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