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Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations

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  • Damiano Brigo
  • Andrea Pallavicini
  • Vasileios Papatheodorou

Abstract

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, as developed more in detail in Brigo and Capponi (2008), including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include Netting in our examples, although other agreements such as Margining and Collateral are left for future work.

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  • 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.
    • Handle: RePEc:arx:papers:0911.3331
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    3. 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.
    4. Damiano Brigo & Naoufel El-Bachir, 2007. "An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model," ICMA Centre Discussion Papers in Finance icma-dp2007-14, Henley Business School, University of Reading.
    5. Damiano Brigo & Marco Tarenghi, 2009. "Credit Default Swap Calibration and Equity Swap Valuation under Counterparty Risk with a Tractable Structural Model," Papers 0912.3028, arXiv.org.
    6. Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
    7. Christophette Blanchet-Scalliet & Fr'ed'eric Patras, 2008. "Counterparty risk valuation for CDS," Papers 0807.0309, arXiv.org.
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    Citations

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    Cited by:

    1. 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.
    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. Johan Gunnesson & Alberto Fern'andez Mu~noz de Morales, 2014. "Recovering from Derivatives Funding: A consistent approach to DVA, FVA and Hedging," Papers 1403.1086, arXiv.org, revised Apr 2014.
    4. 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.
    5. 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.
    6. 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.
    7. Damiano Brigo & Cristin Buescu & Massimo Morini, 2011. "Impact of the first to default time on Bilateral CVA," Papers 1106.3496, arXiv.org.
    8. Lixin Wu, 2013. "CVA and FVA to Derivatives Trades Collateralized by Cash," Papers 1302.0465, arXiv.org.
    9. Matthias Scherer & Thorsten Schulz, 2016. "Extremal Dependence For Bilateral Credit Valuation Adjustments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-21, November.
    10. 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.
    11. 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.
    12. Johan Gunnesson & Alberto Fern'andez Mu~noz de Morales, 2014. "A Bond Consistent Derivative Fair Value," Papers 1406.5755, arXiv.org, revised Sep 2014.
    13. Chris Kenyon, 2010. "Completing CVA and Liquidity: Firm-Level Positions and Collateralized Trades," Papers 1009.3361, arXiv.org.
    14. 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.

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