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Dangerous Knowledge: Credit Value Adjustment With Credit Triggers

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  • CHUANG YI

    (Market and Trading Credit Risk, RBC Capital Market, 200 Bay St., Toronto, ON, Canada, M5J 2W7, Canada)

Abstract

We generalize the arbitrage-free valuation framework for counterparty credit risk (CCR) adjustments when credit triggers are allowed in the contract. The settlement of the deal for the investor could be either obliged or optional to execute when the counterparty hits the credit trigger before any default events from the two parties. General formulas for credit value adjustment (CVA) are given for all four cases: obliged unilateral, obliged bilateral, optional unilateral and optional bilateral. The unilateral CVA with an optional credit trigger is found to be the same as the unilateral CVA with an analogous obliged credit trigger. We show that adding credit triggers will decrease the unilateral CVA for both obliged and optional cases, which are in line with the motivation of investors to reduce CCR. However, adding credit triggers may not necessarily reduce bilateral CVA. Counter-intuitively, we show that the bilateral CVA may actually increase by adding credit triggers. Moreover, the increased amount of bilateral CVA due to credit triggers for one party is exactly the same amount of bilateral CVA reduced for the other party. The CVA calculation is subjected to large uncertainty of model risks, mostly due to the lack of data for calibrating jump-to-default probabilities. Some explicit models for obliged unilateral CVA are discussed with special caveats on the model assumptions. Numerical examples are also given to illustrate the model risk of CVA calculation due to the uncertainty of jump sizes, even though pure jump models are assumed.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:06:n:s0219024911006395
    DOI: 10.1142/S0219024911006395
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    References listed on IDEAS

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    1. Damiano Brigo & Agostino Capponi, 2008. "Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps," Papers 0812.3705, arXiv.org, revised Nov 2009.
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    Cited by:

    1. 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.
    2. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler, 2012. "Collateralized CVA Valuation with Rating Triggers and Credit Migrations," Papers 1205.6542, arXiv.org.
    3. Cyril Durand & Marek Rutkowski, 2013. "CVA for Bilateral Counterparty Risk under Alternative Settlement Conventions," Papers 1307.6486, arXiv.org.

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