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A Note on Discounting and Funding Value Adjustments for Derivatives

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

    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.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 44495.

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    Date of creation: 18 Feb 2013
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    Handle: RePEc:pra:mprapa:44495

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    Related research

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

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    1. 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.
    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, 02.
    3. 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.
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