IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1302.0465.html
   My bibliography  Save this paper

CVA and FVA to Derivatives Trades Collateralized by Cash

Author

Listed:
  • Lixin Wu

Abstract

In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation (PDE) for the derivatives price, obtain and decompose its solution into the risk-free value of the derivative plus credit valuation adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives, as we shall show, CVAs can be evaluated analytically or semi-analytically, while FVAs, as well as the derivatives values, will have to be solved recursively through numerical procedures due to their interdependence. In numerical demonstrations, continuous and discrete margin revisions are considered, respectively, for an equity call option and a vanilla interest-rate swaps.

Suggested Citation

  • Lixin Wu, 2013. "CVA and FVA to Derivatives Trades Collateralized by Cash," Papers 1302.0465, arXiv.org.
    • Handle: RePEc:arx:papers:1302.0465
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1302.0465
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2009. "Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations," Papers 0911.3331, arXiv.org, revised Feb 2010.
    2. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    3. 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.
    4. 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, arXiv.org, revised Dec 2011.
    5. Brian Huge & David Lando, 1999. "Swap Pricing with Two-Sided Default Risk in a Rating-Based Model," Review of Finance, European Finance Association, vol. 3(3), pages 239-268.
    6. Damiano Brigo & Agostino Capponi & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting," Papers 1101.3926, arXiv.org.
    7. Masaaki Fujii & Akihiko Takahashi, 2010. "Choice of Collateral Currency," CIRJE F-Series CIRJE-F-778, CIRJE, Faculty of Economics, University of Tokyo.
    8. Fries, Christian P., 2010. "Discounting Revisited. Valuations under Funding Costs, Counterparty Risk and Collateralization," MPRA Paper 23082, University Library of Munich, Germany, revised 30 May 2010.
    9. Duffie, Darrell & Huang, Ming, 1996. "Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Damiano Brigo, 2011. "Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending," Papers 1111.1331, arXiv.org, revised Jun 2012.
    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. Damiano Brigo & Qing Liu & Andrea Pallavicini & David Sloth, 2014. "Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes," Papers 1404.7314, arXiv.org.
    4. Lixin Wu, 2015. "Cva And Fva To Derivatives Trades Collateralized By Cash," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-22.
    5. 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.
    6. 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, arXiv.org, revised Dec 2011.
    7. Damiano Brigo & Cristin Buescu & Andrea Pallavicini & Qing Liu, 2012. "Illustrating a problem in the self-financing condition in two 2010-2011 papers on funding, collateral and discounting," Papers 1207.2316, arXiv.org, revised Jul 2012.
    8. Damiano Brigo & Andrea Pallavicini, 2013. "CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?," Papers 1312.0128, arXiv.org, revised Dec 2013.
    9. 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.
    10. Yining Ding & Ruyi Liu & Marek Rutkowski, 2024. "Cross-Currency Basis Swaps Referencing Backward-Looking Rates," Papers 2410.08477, arXiv.org.
    11. Damiano Brigo & Cristin Buescu & Massimo Morini, 2011. "Impact of the first to default time on Bilateral CVA," Papers 1106.3496, arXiv.org.
    12. Claudio Albanese & Damiano Brigo & Frank Oertel, 2013. "Restructuring Counterparty Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-29.
    13. 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.
    14. 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.
    15. Damiano Brigo & Cyril Durand, 2014. "An initial approach to Risk Management of Funding Costs," Papers 1410.2034, arXiv.org.
    16. Tomasz R. Bielecki & Marek Rutkowski, 2013. "Valuation and hedging of OTC contracts with funding costs, collateralization and counterparty credit risk: Part 1," Papers 1306.4733, arXiv.org, revised Jun 2013.
    17. Xiao, Tim, 2018. "Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment," EconStor Preprints 202549, ZBW - Leibniz Information Centre for Economics.
    18. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    19. Masaaki Fujii & Akihiko Takahashi, 2015. "Choice of Collateral Currency Updated--A market model for the benchmark pricing--," CIRJE F-Series CIRJE-F-988, CIRJE, Faculty of Economics, University of Tokyo.
    20. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1302.0465. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.