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A Note on Discounting and Funding Value Adjustments for Derivatives


  • Han, Meng
  • He, Yeqi
  • Zhang, Hu


In this paper, valuation of a derivative partially collateralized in a specific foreign currency defined in its credit support annex traded between default-free counterparties is studied. Two pricing approaches -- by hedging and by expectation -- are presented to obtain the same valuation formulae. Our findings show that the current marking-to-market value of such a derivative consists of three components: the price of the perfectly collateralized derivative (a.k.a. price by collateral rate discounting), the value adjustment due to different funding spreads between the payoff currency and the collateral currency, and the value adjustment due to funding requirements of the uncollateralized exposure. These results generalize previous works on discounting for fully collateralized derivatives and on funding value adjustment for partially collateralized or uncollateralized derivatives.

Suggested Citation

  • Han, Meng & He, Yeqi & Zhang, Hu, 2013. "A Note on Discounting and Funding Value Adjustments for Derivatives," MPRA Paper 44495, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:44495

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    References listed on IDEAS

    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 & Yasufumi Shimada & Akihiko Takahashi, 2010. "Collateral Posting and Choice of Collateral Currency - Implications for Derivative Pricing and Risk Management-," CIRJE F-Series CIRJE-F-743, CIRJE, Faculty of Economics, University of Tokyo.
    3. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2011. "Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation," Papers 1112.1521,, revised Dec 2011.
    4. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Note on Construction of Multiple Swap Curves with and without Collateral," CARF F-Series CARF-F-154, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2010.
    5. Hull, John & White, Alan, 2013. "Credit Derivatives," Handbook of the Economics of Finance, Elsevier.
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    More about this item


    CSA; collateral; foreign collateral; derivative pricing; hedging; martingale pricing; FVA; funding cost; funding and discounting;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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