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Disentangling wrong-way risk: Pricing credit valuation adjustment via change of measures

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  • Damiano Brigo
  • Frédéric Vrins

Abstract

In many financial contracts (and in particular when trading OTC derivatives), participants are exposed to counterparty risk. The latter is typically rewarded by adjusting the “risk-free price” of derivatives; an adjustment known as credit value adjustment (CVA). A key driver of CVA is the dependency between exposure and counterparty risk, known as wrong-way risk (WWR). In practice however, correctly addressing WWR is very challenging and calls for heavy numerical techniques. This might explain why WWR is not explicitly handled in the Basel III regulatory framework in spite of its acknowledged importance. In this paper we propose a sound and tractable method to deal efficiently with WWR. Our approach consists in embedding the WWR effect in the drift of the exposure dynamics. Even though this calls for infinite changes of measures, we end up with an appealing compromise between tractability and mathematical rigor, preserving the level of accuracy typically required for CVA figures. The good performances of the method are discussed in a stochastic-intensity default setup based on extensive comparisons of expected positive exposure (EPE) profiles and CVA figures produced (i) by a full bivariate Monte Carlo implementation of the initial model with (ii) our drift-adjustment technique.
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Suggested Citation

  • Damiano Brigo & Frédéric Vrins, 2018. "Disentangling wrong-way risk: Pricing credit valuation adjustment via change of measures," LIDAM Reprints CORE 2949, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:2949
    Note: In : European Journal of Operations Research, 269, 1154-1164, 2018
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    1. Roberto Baviera & Gaetano La Bua & Paolo Pellicioli, 2016. "A note on CVA and wrong way risk," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 1-14, June.
    2. Monique Jeanblanc & Frédéric Vrins, 2018. "Conic martingales from stochastic integrals," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 516-535, April.
    3. Kim, Jinbeom & Leung, Tim, 2016. "Pricing derivatives with counterparty risk and collateralization: A fixed point approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 525-539.
    4. Frédéric Vrins, 2017. "Wrong-Way Risk Cva Models With Analytical Epe Profiles Under Gaussian Exposure Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-35, November.
    5. Cyril Durand & Marek Rutkowski, 2013. "Cva Under Alternative Settlement Conventions And With Systemic Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-40.
    6. Lixin Wu, 2015. "Cva And Fva To Derivatives Trades Collateralized By Cash," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-22.
    7. Cyril Durand & Marek Rutkowski, 2013. "CVA for Bilateral Counterparty Risk under Alternative Settlement Conventions," Papers 1307.6486, arXiv.org.
    8. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    9. Damiano Brigo & Agostino Capponi & Andrea Pallavicini & Vasileios Papatheodorou, 2013. "Pricing Counterparty Risk Including Collateralization, Netting Rules, Re-Hypothecation And Wrong-Way Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-16.
    10. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
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    Citations

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    Cited by:

    1. Cheikh Mbaye & Frédéric Vrins, 2022. "Affine term structure models: A time‐change approach with perfect fit to market curves," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 678-724, April.
    2. F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "CVA and vulnerable options pricing by correlation expansions," Annals of Operations Research, Springer, vol. 299(1), pages 401-427, April.
    3. Marc Chataigner & Stéphane Crépey, 2019. "Credit Valuation Adjustment Compression by Genetic Optimization," Risks, MDPI, vol. 7(4), pages 1-21, September.
    4. Ketelbuters, John-John & Hainaut, Donatien, 2022. "CDS pricing with fractional Hawkes processes," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1139-1150.
    5. E. Alòs & F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "Cva And Vulnerable Options In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-34, March.
    6. Alòs, Elisa & Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2023. "CVA in fractional and rough volatility models," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    7. Ashish Kumar & Laszlo Markus & Norbert Hari, 2021. "Arbitrage-free pricing of CVA for cross-currency swap with wrong-way risk under stochastic correlation modeling framework," Papers 2107.06349, arXiv.org.
    8. Ballotta, Laura & Fusai, Gianluca & Marazzina, Daniele, 2019. "Integrated structural approach to Credit Value Adjustment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1143-1157.
    9. Elisa Al`os & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2022. "CVA in fractional and rough volatility models," Papers 2204.11554, arXiv.org.
    10. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "An arbitrage-free conic martingale model with application to credit risk," Papers 1909.02474, arXiv.org.
    11. Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2022. "Approximate value adjustments for European claims," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1149-1161.
    12. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2020. "A moment matching method for option pricing under stochastic interest rates," Papers 2005.14063, arXiv.org.
    13. Castellano, Rosella & Corallo, Vincenzo & Morelli, Giacomo, 2022. "Structural estimation of counterparty credit risk under recovery risk," Journal of Banking & Finance, Elsevier, vol. 140(C).
    14. Deelstra, Griselda & Hieber, Peter, 2023. "Randomization and the valuation of guaranteed minimum death benefits," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1218-1236.
    15. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2022. "Computing XVA for American basket derivatives by Machine Learning techniques," Papers 2209.06485, arXiv.org.
    16. Erdinc Akyildirim & Alper A. Hekimoglu & Ahmet Sensoy & Frank J. Fabozzi, 2023. "Extending the Merton model with applications to credit value adjustment," Annals of Operations Research, Springer, vol. 326(1), pages 27-65, July.

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