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CVA in fractional and rough volatility models

Author

Listed:
  • Elisa Al`os
  • Fabio Antonelli
  • Alessandro Ramponi
  • Sergio Scarlatti

Abstract

In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with the default event. We specialize it for some volatility models and we provide price approximations, based on the representation formula. We study numerically their accuracy, comparing the results with Monte Carlo simulations, and we run a theoretical study of the error. We also introduce a seminal study of roughness influence on the claim's price.

Suggested Citation

  • Elisa Al`os & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2022. "CVA in fractional and rough volatility models," Papers 2204.11554, arXiv.org.
    • Handle: RePEc:arx:papers:2204.11554
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    References listed on IDEAS

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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. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    3. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver - A neural network based counterparty credit risk management framework," Working Papers 07/2020, University of Verona, Department of Economics.
    4. Fard, Farzad Alavi, 2015. "Analytical pricing of vulnerable options under a generalized jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 19-28.
    5. 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.
    6. 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.
    7. Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October.
    8. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. 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.
    11. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    12. 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..
    13. Elisa Alòs & Kenichiro Shiraya, 2019. "Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach," Finance and Stochastics, Springer, vol. 23(2), pages 423-447, April.
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