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Wrong-Way Risk Adjusted Exposure: Analytical Approximations for Options in Default Intensity Models

In: Innovations in Insurance, Risk- and Asset Management

Author

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  • Damiano Brigo
  • Thomas Hvolby
  • Frédéric Vrins

Abstract

We examine credit value adjustment (CVA) estimation under wrong-way risk (WWR) by computing the expected positive exposure (EPE) under an equivalent measure as suggested in [1], adjusting the drift of the underlying for default risk. We apply this technique to European put and call options and derive the analytic formulas for EPE under WWR obtained with various approximations of the drift adjustment. We give the results of numerical experiments based on 4 parameter sets, and supply figures of the CVA based on both of the suggested proxys, comparing with CVA based on a 2D-Monte Carlo scheme and Gaussian Copula resampling. We also show the CVA obtained by the formulas from Basel III. We observe that the Basel III formula does not account for the credit-market correlation, while the Gaussian Copula resampling method estimates a too large impact of this correlation. The two proxies account for the credit-market correlation, and give results that are mostly similar to the 2D-Monte Carlo results.

Suggested Citation

  • Damiano Brigo & Thomas Hvolby & Frédéric Vrins, 2018. "Wrong-Way Risk Adjusted Exposure: Analytical Approximations for Options in Default Intensity Models," World Scientific Book Chapters, in: Kathrin Glau & Daniël Linders & Aleksey Min & Matthias Scherer & Lorenz Schneider & Rudi Zagst (ed.), Innovations in Insurance, Risk- and Asset Management, chapter 2, pages 27-45, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789813272569_0002
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Alòs, Elisa & Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2023. "CVA in fractional and rough volatility models," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    5. Elisa Al`os & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2022. "CVA in fractional and rough volatility models," Papers 2204.11554, arXiv.org.

    More about this item

    Keywords

    Insurance; Actuarial Science; Risk Measure; Reinsurance; Copula; Replicating Portfolio; Bayesian Finance; Risk Classification; Stochastic Dominance; Dynamic Hedging; Autoregressive Hidden Markov Models; Exchange-Traded Funds; Uncertainty Quantification; Fixed Income; Stochastic Processes for Finance;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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