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A Note On The Self-Financing Condition For Funding, Collateral And Discounting

Author

Listed:
  • DAMIANO BRIGO

    (Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, UK)

  • CRISTIN BUESCU

    (Department of Mathematics, King's College London, Strand, London, WC2R 2LS, UK)

  • ANDREA PALLAVICINI

    (Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, UK)

  • QING LIU

    (Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, UK)

Abstract

We present the derivation of the self-financing condition used in a derivative pricing framework with funding, collateral and discounting. This is done in a way that clarifies the structure of the relevant funding accounts. This clarification is achieved by properly distinguishing between price processes, dividend processes and gains processes. Without this explicit distinction, the resulting self-financing condition can be erroneous, as we illustrate in the case of two papers: Piterbarg (2010) and Burgard & Kjaer (2011a). In these papers, the self-financing condition is equivalent to assuming that a subportfolio is self-financing on its own and without including the cash position. We show that the final result in Piterbarg (2010) is correct, even if the related self-financing condition is not. In the process, we raise a further question on the supplementary source of randomness in the funding rate dynamics that has no hedging counterpart in the replicating portfolio.

Suggested Citation

  • Damiano Brigo & Cristin Buescu & Andrea Pallavicini & Qing Liu, 2015. "A Note On The Self-Financing Condition For Funding, Collateral And Discounting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-10.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:02:n:s0219024915500119
    DOI: 10.1142/S0219024915500119
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    References listed on IDEAS

    as
    1. Tomasz R. Bielecki & Marek Rutkowski, 2014. "Valuation and Hedging of Contracts with Funding Costs and Collateralization," Papers 1405.4079, arXiv.org, revised Dec 2014.
    2. Masaaki Fujii & Akihiko Takahashi, 2010. "Choice of Collateral Currency," CARF F-Series CARF-F-239, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2012. "Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments," Papers 1210.3811, arXiv.org, revised Dec 2012.
    4. 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.
    5. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2010. "Collateral Posting and Choice of Collateral Currency -Implications for Derivative Pricing and Risk Management-," CARF F-Series CARF-F-216, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Masaaki Fujii & Akihiko Takahashi, 2010. "Choice of Collateral Currency," CIRJE F-Series CIRJE-F-778, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

    1. Alessandro Gnoatto & Nicole Seiffert, 2020. "Cross Currency Valuation and Hedging in the Multiple Curve Framework," Papers 2001.11012, arXiv.org, revised Mar 2021.

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