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Arbitrage-Free Valuation Of Bilateral Counterparty Risk For Interest-Rate Products: Impact Of Volatilities And Correlations

Author

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  • DAMIANO BRIGO

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

  • ANDREA PALLAVICINI

    (Financial Engineering, Mediobanca, Piazzetta Cuccia 1, Milano, 20121, Italy)

  • VASILEIOS PAPATHEODOROU

    (Barclays Capital, London, EC3P 3AH, UK)

Abstract

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustment (CVA) 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, 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 close-out netting rules in our examples, although other agreements, such as periodic margining or collateral posting, are left for future work.

Suggested Citation

  • Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Arbitrage-Free Valuation Of Bilateral Counterparty Risk For Interest-Rate Products: Impact Of Volatilities And Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 773-802.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:06:n:s0219024911006759
    DOI: 10.1142/S0219024911006759
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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, revised Mar 2025.
    2. Monique Jeanblanc & Libo Li & Shiqi Song, 2018. "An enlargement of filtration formula with applications to multiple non-ordered default times," Finance and Stochastics, Springer, vol. 22(1), pages 205-240, January.
    3. Tavasoli, Ahmadreza & Breton, Michèle, 2025. "Evaluation of counterparty credit risk under netting agreements," European Journal of Operational Research, Elsevier, vol. 320(2), pages 402-416.
    4. 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.
    5. Kenichiro Shiraya & Akihiko Takahashi, 2016. "Price impacts of imperfect collateralization," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-31, March.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Price Impacts of Imperfect Collateralization," CIRJE F-Series CIRJE-F-947, CIRJE, Faculty of Economics, University of Tokyo.
    7. 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.
    8. van der Zwaard, Thomas & Grzelak, Lech A. & Oosterlee, Cornelis W., 2021. "A computational approach to hedging Credit Valuation Adjustment in a jump-diffusion setting," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    9. Ayoub Gargouri & Van Son Lai & Issouf Soumaré, 2016. "Revisiting Interest Rate Swap Valuation with Counterparty Risk, Wrong-Way Risk and OIS Discount," Working Papers 2016-003, Department of Research, Ipag Business School.
    10. T. van der Zwaard & L. A. Grzelak & C. W. Oosterlee, 2022. "Relevance of Wrong-Way Risk in Funding Valuation Adjustments," Papers 2204.02680, arXiv.org, revised Jun 2022.
    11. van der Zwaard, Thomas & Grzelak, Lech A. & Oosterlee, Cornelis W., 2022. "Relevance of Wrong-Way Risk in Funding Valuation Adjustments," Finance Research Letters, Elsevier, vol. 49(C).
    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. 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.
    14. Francesca Biagini & Alessandro Gnoatto & Katharina Oberpriller, 2025. "When defaults cannot be hedged: an actuarial approach to xVA calculations via local risk-minimization," Papers 2502.12774, arXiv.org, revised Feb 2025.
    15. 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.
    16. Lorenzo Silotto & Marco Scaringi & Marco Bianchetti, 2024. "XVA modelling: validation, performance and model risk management," Annals of Operations Research, Springer, vol. 336(1), pages 183-274, May.
    17. 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.
    18. Joel P. Villarino & 'Alvaro Leitao & Jos'e A. Garc'ia-Rodr'iguez, 2022. "Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk," Papers 2210.02175, arXiv.org.
    19. P. Amster & A. P. Mogni, 2018. "Adapting the CVA model to Leland's framework," Papers 1802.04837, arXiv.org.
    20. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Price Impacts of Imperfect Collateralization," CARF F-Series CARF-F-355, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2015.
    21. 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.
    22. Kristoffer Andersson & Alessandro Gnoatto, 2025. "Multi-Layer Deep xVA: Structural Credit Models, Measure Changes and Convergence Analysis," Papers 2502.14766, arXiv.org, revised Feb 2025.
    23. T. van der Zwaard & L. A. Grzelak & C. W. Oosterlee, 2022. "Efficient Wrong-Way Risk Modelling for Funding Valuation Adjustments," Papers 2209.12222, arXiv.org, revised Jun 2024.

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