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Collateralized Cva Valuation With Rating Triggers And Credit Migrations

Author

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  • TOMASZ R. BIELECKI

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616 IL, USA)

  • IGOR CIALENCO

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616 IL, USA)

  • ISMAIL IYIGUNLER

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616 IL, USA)

Abstract

In this paper we discuss the issue of computation of the bilateral credit valuation adjustment (CVA) under rating triggers, and in presence of ratings-linked margin agreements. Specifically, we consider collateralized OTC contracts, that are subject to rating triggers, between two parties — an investor and a counterparty. Moreover, we model the margin process as a functional of the credit ratings of the counterparty and the investor. We employ a Markovian approach for modeling of the rating transitions of the two parties to the contract. In this framework, we derive the representation for bilateral CVA. We also introduce a new component in the decomposition of the counterparty risky price: namely the rating valuation adjustment (RVA) that accounts for the rating triggers. We give two examples of dynamic collateralization schemes where the margin thresholds are linked to the credit ratings of the parties. Our results are illustrated via computation of various counterparty risk adjustments for a CDS contract and for an IRS contract.

Suggested Citation

  • Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler, 2013. "Collateralized Cva Valuation With Rating Triggers And Credit Migrations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-32.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:02:n:s021902491350009x
    DOI: 10.1142/S021902491350009X
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    References listed on IDEAS

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    1. Zhou, Richard, 2010. "Counterparty Risk Subject To ATE," MPRA Paper 28067, University Library of Munich, Germany.
    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. Zhou, Richard, 2010. "Counterparty Risk Subject To ATE," MPRA Paper 27782, University Library of Munich, Germany.
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    Citations

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    Cited by:

    1. Xiao,Tim, 2018. "Pricing Financial Derivatives Subject to Multilateral Credit Risk and Collateralization," EconStor Preprints 202075, ZBW - Leibniz Information Centre for Economics.
    2. White, Alan, 2018. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," MPRA Paper 85331, University Library of Munich, Germany.
    3. Xiao, Tim, 2018. "The Valuation of Credit Default Swap with Counterparty Risk and Collateralization," EconStor Preprints 203447, ZBW - Leibniz Information Centre for Economics.
    4. Boros, Péter, 2020. "A hitelminősítői bejelentések fertőző hatásai és a hitelértékelési kiigazítás [Rating migration, credit risk contagion and Credit Valuation Adjustment]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(2), pages 140-163.
    5. Alan White, 2018. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," Papers 1803.07843, arXiv.org.
    6. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2022. "Nonlinear Valuation with XVAs: Two Converging Approaches," Mathematics, MDPI, vol. 10(5), pages 1-31, March.
    7. Tim, Xiao, 2019. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," MPRA Paper 94701, University Library of Munich, Germany.
    8. Alan White, 2018. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," Working Papers hal-01739310, HAL.
    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. Damiano Brigo & Federico Graceffa & Alexander Kalinin, 2021. "Mild to classical solutions for XVA equations under stochastic volatility," Papers 2112.11808, arXiv.org.

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