IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1106.3496.html
   My bibliography  Save this paper

Impact of the first to default time on Bilateral CVA

Author

Listed:
  • Damiano Brigo
  • Cristin Buescu
  • Massimo Morini

Abstract

We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representation of bilateral risk and ignores that upon the first default closeout proceedings are ignited. As such, it involves double counting. We compare this formula with the fully specified bilateral risk formula, where the first to default time is taken into account. The latter correct formula depends on default dependence between the two parties, whereas the simplified one does not. We also analyze a candidate simplified formula in case the replacement closeout is used upon default, following ISDA's recommendations, and we find the simplified formula to be the same as in the risk free closeout case. We analyze the error that is encountered when using the simplified formula in a couple of simple products: a zero coupon bond, where the exposure is unidirectional, and an equity forward contract where exposure can go both ways. For the latter case we adopt a bivariate exponential distribution due to Gumbel to model the joint default risk of the two parties in the deal. We present a number of realistic cases where the simplified formula differs considerably from the correct one.

Suggested Citation

  • Damiano Brigo & Cristin Buescu & Massimo Morini, 2011. "Impact of the first to default time on Bilateral CVA," Papers 1106.3496, arXiv.org.
  • Handle: RePEc:arx:papers:1106.3496
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1106.3496
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Damiano Brigo & Massimo Morini, 2010. "Dangers of Bilateral Counterparty Risk: the fundamental impact of closeout conventions," Papers 1011.3355, arXiv.org.
    2. 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.
    3. 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.
    4. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 209-238, November.
    5. Damiano Brigo & Agostino Capponi, 2008. "Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps," Papers 0812.3705, arXiv.org, revised Nov 2009.
    6. 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. Lorenzo Giada & Claudio Nordio, 2012. "Funded Bilateral Valuation Adjustment," Papers 1211.1564, arXiv.org.
    2. 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.
    3. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
    4. 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.
    5. 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.
    6. Zhou, Richard, 2015. "Exact Methods for Path-Dependent Credit Exposure," MPRA Paper 64647, University Library of Munich, Germany, revised 25 May 3025.
    7. Zhou, Richard, 2015. "Modeling Path Dependent Counterparty Credit Risk," MPRA Paper 61354, University Library of Munich, Germany.
    8. Lorenzo Giada & Claudio Nordio, 2012. "Bilateral Credit Valuation Adjustment of an Optional Early Termination Clause," Papers 1205.2013, arXiv.org, revised Jan 2013.

    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. 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.
    3. 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.
    4. Lixin Wu, 2013. "CVA and FVA to Derivatives Trades Collateralized by Cash," Papers 1302.0465, arXiv.org.
    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. Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2009. "Credit models and the crisis, or: how I learned to stop worrying and love the CDOs," Papers 0912.5427, arXiv.org, revised Feb 2010.
    7. Damiano Brigo & Massimo Morini & Marco Tarenghi, 2009. "Credit Calibration with Structural Models: The Lehman case and Equity Swaps under Counterparty Risk," Papers 0912.4404, arXiv.org.
    8. Arregui, Iñigo & Salvador, Beatriz & Vázquez, Carlos, 2017. "PDE models and numerical methods for total value adjustment in European and American options with counterparty risk," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 31-53.
    9. Sakurai, Yuji & Uchida, Yoshihiko, 2014. "Rehypothecation dilemma: Impact of collateral rehypothecation on derivative prices under bilateral counterparty credit risk," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 361-373.
    10. Calice, Giovanni, 2011. "The Impact of Collateral Policies on Sovereign CDS Spreads," ECMI Papers 12234, Centre for European Policy Studies.
    11. 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.
    12. 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.
    13. 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.
    14. Loon, Yee Cheng & Zhong, Zhaodong Ken, 2014. "The impact of central clearing on counterparty risk, liquidity, and trading: Evidence from the credit default swap market," Journal of Financial Economics, Elsevier, vol. 112(1), pages 91-115.
    15. Cousin, Areski & Laurent, Jean-Paul, 2008. "Comparison results for exchangeable credit risk portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1118-1127, June.
    16. Gupta, Anurag & Subrahmanyam, Marti G., 2000. "An empirical examination of the convexity bias in the pricing of interest rate swaps," Journal of Financial Economics, Elsevier, vol. 55(2), pages 239-279, February.
    17. Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2011. "Bivariate Semi-Markov Process for Counterparty Credit Risk," Papers 1112.0226, arXiv.org, revised Oct 2012.
    18. Hans Dewachter & Marco Lyrio & Konstantijn Maes, 2004. "The Effect of Monetary Unification on German Bond Markets," European Financial Management, European Financial Management Association, vol. 10(3), pages 487-509, September.
    19. Xiao, Tim, 2012. "An Economic Examination of Collateralization in Different Financial Markets," MPRA Paper 47105, University Library of Munich, Germany.
    20. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Yang, Xinda, 2021. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 9-24.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1106.3496. See general information about how to correct material in RePEc.

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

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.