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Counterparty Risk and Funding: The Four Wings of the TVA

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  • St'ephane Cr'epey
  • R'emi Gerboud
  • Zorana Grbac
  • Nathalie Ngor

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 [Cr12a] and [Cr12b]. 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, also allowing one to assess the related model risk issue.

Suggested Citation

  • St'ephane Cr'epey & R'emi Gerboud & Zorana Grbac & Nathalie Ngor, 2012. "Counterparty Risk and Funding: The Four Wings of the TVA," Papers 1210.5046, arXiv.org.
    • Handle: RePEc:arx:papers:1210.5046
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    References listed on IDEAS

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    1. 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.
    2. Stéphane Crépey & Raphaël Douady, 2014. "The Whys of the LOIS: Credit Skew and Funding Spread Volatility," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01151315, HAL.
    3. Damir FILIPOVIC & Anders B. TROLLE, 2011. "The Term Structure of Interbank Risk," Swiss Finance Institute Research Paper Series 11-34, Swiss Finance Institute.
    4. Masaaki Fujii & Akihiko Takahashi, 2011. "Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA," Papers 1101.5849, arXiv.org, revised Dec 2011.
    5. 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.
    6. 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.
    7. 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.
    8. Masaaki Fujii & Akihiko Takahashi, 2010. "Choice of Collateral Currency," CIRJE F-Series CIRJE-F-778, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

    1. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2015. "Arbitrage-Free Pricing of XVA -- Part I: Framework and Explicit Examples," Papers 1501.05893, arXiv.org, revised Aug 2016.
    2. Kun Tian & Dewen Xiong & Wenchao Yan & George Xianzhi Yuan, 2018. "The study of dynamics for credit default risk by backward stochastic differential equation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-32, December.

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