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Collateralized CVA Valuation with Rating Triggers and Credit Migrations

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  • Tomasz R. Bielecki
  • Igor Cialenco
  • Ismail Iyigunler

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. We account for the rehypothecation risk in the presence of independent amounts. 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, 2012. "Collateralized CVA Valuation with Rating Triggers and Credit Migrations," Papers 1205.6542, arXiv.org.
    • Handle: RePEc:arx:papers:1205.6542
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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. Chuang Yi, 2011. "Dangerous Knowledge: Credit Value Adjustment With Credit Triggers," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 839-865.
    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. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler, 2011. "Counterparty Risk and the Impact of Collateralization in CDS Contracts," Papers 1104.2625, arXiv.org, revised Aug 2011.
    5. Zhou, Richard, 2010. "Counterparty Risk Subject To ATE," MPRA Paper 27782, University Library of Munich, Germany.
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    1. Bielecki, Tomasz R. & Cousin, Areski & Crépey, Stéphane & Herbertsson, Alexander, 2011. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model (Previous title: Dynamic Modeling of Portfolio Credit Risk with Common Shocks)," Working Papers in Economics 502, University of Gothenburg, Department of Economics, revised 12 Oct 2012.

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