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Wrong-Way Risk CVA Models with Analytical EPE Profiles under Gaussian Exposure Dynamics

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  • Vrins, Frédéric

Abstract

We consider two classes of wrong-way risk models in the context of CVA: static (resampling) and dynamic (reduced form). Although both potentially suffer from arbitrage problems, their tractability makes them appealing to the industry and therefore deserve additional study. For example, Gaussian copula-based resampling and reduced-form with “Hull–White intensities” yield analytical expected positive exposure (EPE) profiles when the portfolio price process (i.e. exposure process) is Gaussian. However, the first approach disregards credit volatility whilst the second can provide default probabilities larger than 1. We therefore enlarge the study by introducing a new dynamic approach for credit risk, consisting in the straight modeling of the survival (Azéma supermartingale) process using the Φ-martingale. This method is appealing in that it helps fixing some drawbacks of the above models. Indeed, it is a dynamic method (it disentangles correlation and credit volatility) that preserves probabilities in [0, 1] without affecting the analytical tractability of the model. In particular, calibration to any valid default probability curve is automatic and the closed-form expression for the EPE profiles remains available under Gaussian exposures. For each approach, we derive analytically the EPE profiles (conditional upon default) associated to prototypical exposure processes of Forward Rate Agreement (FRA) and Interest Rate Swap (IRS) in all cases and provide a comparison and discuss the implied Credit Valuation Adjustment (CVA) figures.
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Suggested Citation

  • Vrins, Frédéric, 2017. "Wrong-Way Risk CVA Models with Analytical EPE Profiles under Gaussian Exposure Dynamics," LIDAM Reprints LFIN 2017001, Université catholique de Louvain, Louvain Finance (LFIN).
    • Handle: RePEc:ajf:louvlr:2017001
    Note: In : International Journal of Theoretical and Applied Finance, Vol. 20, no. 7:1750045 (2017)
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    References listed on IDEAS

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    1. Monique Jeanblanc & Frédéric Vrins, 2018. "Conic martingales from stochastic integrals," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 516-535, April.
    2. Damiano Brigo & Fr'ed'eric Vrins, 2016. "Disentangling wrong-way risk: pricing CVA via change of measures and drift adjustment," Papers 1611.02877, arXiv.org.
    3. 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.
    4. Rafael Mendoza-Arriaga & Vadim Linetsky, 2014. "Time-changed CIR default intensities with two-sided mean-reverting jumps," Papers 1403.5402, arXiv.org.
    5. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
    6. Samim Ghamami, 2013. "Counterparty Credit Risk," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1863-1865, December.
    7. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    8. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    9. Vrins, F. & Jeanblanc, M., 2015. "The [phi]-Martingale," LIDAM Discussion Papers CORE 2015022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. S. Crépey & M. Jeanblanc & D. Wu, 2013. "Informationally Dynamized Gaussian Copula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-29.
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    1. BRIGO, Damiano & VRINS, Frédéric, 2018. "Disentangling wrong-way risk: pricing credit valuation adjustment via change of measures," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1154-1164.
    2. Cheikh Mbaye & Frédéric Vrins, 2018. "A Subordinated Cir Intensity Model With Application To Wrong-Way Risk Cva," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-22, November.
    3. 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.

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