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Counterparty Risk And Funding: The Four Wings Of The Tva

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  • STÉPHANE CRÉPEY

    (Laboratoire Analyse et Probabilités, Université d'Évry Val d'Essonne, 91037 Évry Cedex, France)

  • RÉMI GERBOUD

    (Laboratoire Analyse et Probabilités, Université d'Évry Val d'Essonne, 91037 Évry Cedex, France)

  • ZORANA GRBAC

    (Laboratoire Analyse et Probabilités, Université d'Évry Val d'Essonne, 91037 Évry Cedex, France)

  • NATHALIE NGOR

    (Laboratoire Analyse et Probabilités, Université d'Évry Val d'Essonne, 91037 Évry Cedex, France)

Abstract

The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related credit valuation adjustment (CVA), debt valuation adjustment (DVA), liquidity valuation adjustment (LVA) and replacement cost (RC) issues, jointly referred to in this paper as total valuation adjustment (TVA), have been thoroughly investigated in the theoretical papers [8, 9]. The present work provides an executive summary and numerical companion to these papers, through which the TVA pricing problem can be reduced to Markovian pre-default TVA BSDEs. The first step consists in the counterparty clean valuation of a portfolio of contracts, which is the valuation in a hypothetical situation where the two parties would be risk-free and funded at a risk-free rate. In the second step, the TVA is obtained as the value of an option on the counterparty clean value process called contingent credit default swap (CCDS). Numerical results are presented for interest rate swaps in the Vasicek, as well as in the inverse Gaussian Hull-White short rate model, which allows also to assess the related model risk issue.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:02:n:s0219024913500064
    DOI: 10.1142/S0219024913500064
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    References listed on IDEAS

    as
    1. Stéphane Crépey & Raphaël Douady, 2013. "The Whys of the LOIS: Credit Skew and Funding Rates Volatility," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01477891, HAL.
    2. 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.
    3. 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.
    4. Masaaki Fujii & Akihiko Takahashi, 2011. "Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA," CARF F-Series CARF-F-265, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Masaaki Fujii & Akihiko Takahashi, 2010. "Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA," CARF F-Series CARF-F-240, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Mar 2011.
    6. Masaaki Fujii & Akihiko Takahashi, 2010. "Choice of Collateral Currency," CIRJE F-Series CIRJE-F-778, CIRJE, Faculty of Economics, University of Tokyo.
    7. Masaaki Fujii & Akihiko Takahashi, 2011. "Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA," Papers 1101.5849, arXiv.org, revised Dec 2011.
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    Citations

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    Cited by:

    1. Yannick Armenti & Stéphane Crépey, 2017. "Central Clearing Valuation Adjustment," Working Papers hal-01169169, HAL.
    2. Stephane Crepey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2015. "Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments," Papers 1502.07397, arXiv.org.
    3. Bernard Lapeyre & Marouan Iben Taarit, 2019. "A Forward Equation For Computing Derivatives Exposure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-26, May.
    4. Laura Morino & Wolfgang J. Ruggaldier, 2014. "On multicurve models for the term structure," Papers 1401.5431, arXiv.org.
    5. Christian Bender & Christian Gärtner & Nikolaus Schweizer, 2018. "Pathwise Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 965-965, August.
    6. Stéphane Crépey & Tuyet Mai Nguyen, 2018. "Nonlinear Monte Carlo schemes for counterparty risk on credit derivatives," Working Papers hal-01764400, HAL.
    7. Stéphane Crépey & Shiqi Song, 2018. "Counterparty risk and funding: immersion and beyond," Working Papers hal-01764403, HAL.
    8. Weijie Pang & Stephan Sturm, 2020. "XVA Valuation under Market Illiquidity," Papers 2011.03543, arXiv.org.
    9. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2018. "Risk-neutral valuation under differential funding costs, defaults and collateralization," Papers 1802.10228, arXiv.org.
    10. Stéphane Crépey & Shiqi Song, 2014. "Counterparty risk and funding: Immersion and beyond," Working Papers hal-00989062, HAL.
    11. Yannick Armenti & St'ephane Cr'epey, 2015. "Central Clearing Valuation Adjustment," Papers 1506.08595, arXiv.org, revised Feb 2017.

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