IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v23y2020i01ns0219024920500065.html
   My bibliography  Save this article

xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT

Author

Listed:
  • LIXIN WU

    (Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • DAWEI ZHANG

    (Goldman Sachs (Asia) L.L.C., 68th Floor, Cheung Kong Center, 2 Queen’s Road, Central, Hong Kong)

Abstract

xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

Suggested Citation

  • Lixin Wu & Dawei Zhang, 2020. "xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-24, February.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:01:n:s0219024920500065
    DOI: 10.1142/S0219024920500065
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/abs/10.1142/S0219024920500065
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024920500065?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Patrick Hagan & Diana Woodward, 1999. "Markov interest rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(4), pages 233-260.
    2. Lijun Bo & Agostino Capponi, 2014. "Bilateral credit valuation adjustment for large credit derivatives portfolios," Finance and Stochastics, Springer, vol. 18(2), pages 431-482, April.
    3. Andrew Green & Chris Kenyon, 2014. "MVA: Initial Margin Valuation Adjustment by Replication and Regression," Papers 1405.0508, arXiv.org, revised Jan 2015.
    4. Leif Andersen & Darrell Duffie & Yang Song, 2019. "Funding Value Adjustments," Journal of Finance, American Finance Association, vol. 74(1), pages 145-192, February.
    5. 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.
    6. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.
    7. 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.
    8. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    9. Lixin Wu & Chonhong Li, 2015. "FVA and CVA under margining," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 32(3), pages 298-321, August.
    10. 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.
    11. Stefania Gabrielli & Andrea Pallavicini & Stefano Scoleri, 2019. "Funding Adjustments in Equity Linear Products," Papers 1906.02561, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    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. Junbeom Lee & Chao Zhou, 2021. "Binary funding impacts in derivative valuation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 242-278, January.
    2. Brigo, Damiano & Francischello, Marco & Pallavicini, Andrea, 2019. "Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement," European Journal of Operational Research, Elsevier, vol. 274(2), pages 788-805.
    3. 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.
    4. Lokman A. Abbas-Turki & Stéphane Crépey & Babacar Diallo, 2018. "Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-40, September.
    5. Simonella, Roberta & Vázquez, Carlos, 2023. "XVA in a multi-currency setting with stochastic foreign exchange rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 59-79.
    6. Lixin Wu, 2013. "CVA and FVA to Derivatives Trades Collateralized by Cash," Papers 1302.0465, arXiv.org.
    7. 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.
    8. 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.
    9. Giovanni Mottola, 2014. "Reflected Backward SDE approach to the price-hedge of defaultable claims with contingent switching CSA," Papers 1412.1325, arXiv.org, revised Feb 2015.
    10. Lorenzo Silotto & Marco Scaringi & Marco Bianchetti, 2021. "Everything You Always Wanted to Know About XVA Model Risk but Were Afraid to Ask," Papers 2107.10377, arXiv.org.
    11. Stéphane Crépey & Wissal Sabbagh & Shiqi Song, 2020. "When Capital Is a Funding Source: The Anticipated Backward Stochastic Differential Equations of X-Value Adjustments," Post-Print hal-03910119, HAL.
    12. 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.
    13. Tumasyan, Hovik, 2018. "A Second Look at Post Crisis Pricing of Derivatives - Part I: A Note on Money Accounts and Collateral," MPRA Paper 90806, University Library of Munich, Germany.
    14. 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.
    15. Francesca Biagini & Alessandro Gnoatto & Immacolata Oliva, 2019. "Pricing of counterparty risk and funding with CSA discounting, portfolio effects and initial margin," Working Papers 04/2019, University of Verona, Department of Economics.
    16. Stéphane Crépey, 2022. "Positive XVAs," Post-Print hal-03910135, HAL.
    17. 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.
    18. Giovanni Mottola, 2014. "Generalized Dynkin game of switching type representation for defaultable claims in presence of contingent CSA," Papers 1410.0594, arXiv.org, revised Jan 2015.
    19. Claudio Albanese & Stéphane Crépey & Rodney Hoskinson & Bouazza Saadeddine, 2021. "XVA analysis from the balance sheet," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 99-123, January.
    20. Chris Kenyon & Richard David Kenyon, 2013. "DVA for Assets," Papers 1301.5425, arXiv.org.

    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:wsi:ijtafx:v:23:y:2020:i:01:n:s0219024920500065. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.