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XVA Analysis From the Balance Sheet

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  • Claudio Albanese
  • Stephane Crepey
  • Rodney Hoskinson
  • Bouazza Saadeddine

Abstract

XVAs denote various counterparty risk related valuation adjustments that are applied to financial derivatives since the 2007--09 crisis. We root a cost-of-capital XVA strategy in a balance sheet perspective which is key in identifying the economic meaning of the XVA terms. Our approach is first detailed in a static setup that is solved explicitly. It is then plugged in the dynamic and trade incremental context of a real derivative banking portfolio. The corresponding cost-of-capital XVA strategy ensures to bank shareholders a submartingale equity process corresponding to a target hurdle rate on their capital at risk, consistently between and throughout deals. Set on a forward/backward SDE formulation, this strategy can be solved efficiently using GPU computing combined with deep learning regression methods in a whole bank balance sheet context. A numerical case study emphasizes the workability and added value of the ensuing pathwise XVA computations.

Suggested Citation

  • Claudio Albanese & Stephane Crepey & Rodney Hoskinson & Bouazza Saadeddine, 2020. "XVA Analysis From the Balance Sheet," Papers 2009.00368, arXiv.org.
    • Handle: RePEc:arx:papers:2009.00368
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    Cited by:

    1. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    2. Giorgia Callegaro & Alessandro Gnoatto & Martino Grasselli, 2021. "A Fully Quantization-based Scheme for FBSDEs," Working Papers 07/2021, University of Verona, Department of Economics.
    3. D Barrera & S Cr'epey & E Gobet & Hoang-Dung Nguyen & B Saadeddine, 2022. "Learning Value-at-Risk and Expected Shortfall," Papers 2209.06476, arXiv.org.
    4. Callegaro, Giorgia & Gnoatto, Alessandro & Grasselli, Martino, 2023. "A fully quantization-based scheme for FBSDEs," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    5. Lokman A. Abbas‐Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA regressions with oversimulated defaults," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 274-307, April.
    6. Claudio Albanese & Stéphane Crépey & Stefano Iabichino, 2023. "Quantitative reverse stress testing, bottom up," Quantitative Finance, Taylor & Francis Journals, vol. 23(5), pages 863-875, May.
    7. Stéphane Crépey, 2022. "Positive XVAs," Post-Print hal-03910135, HAL.
    8. Dorinel Bastide & Stéphane Crépey & Samuel Drapeau & Mekonnen Tadese, 2022. "Derivatives Risks as Costs in a One-Period Network Model," Working Papers hal-03554577, HAL.
    9. Simonella, Roberta & Vázquez, Carlos, 2023. "XVA in a multi-currency setting with stochastic foreign exchange rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 59-79.
    10. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    11. D Barrera & S Crépey & E Gobet & Hoang-Dung Nguyen & B Saadeddine, 2022. "Learning Value-at-Risk and Expected Shortfall," Working Papers hal-03775901, HAL.
    12. You-Shyang Chen & Chien-Ku Lin & Chih-Min Lo & Su-Fen Chen & Qi-Jun Liao, 2021. "Comparable Studies of Financial Bankruptcy Prediction Using Advanced Hybrid Intelligent Classification Models to Provide Early Warning in the Electronics Industry," Mathematics, MDPI, vol. 9(20), pages 1-26, October.
    13. Lokman Abbas-Turki & St'ephane Cr'epey & Bouazza Saadeddine, 2022. "Pathwise CVA Regressions With Oversimulated Defaults," Papers 2211.17005, arXiv.org.
    14. Claudio Albanese & Cyril B'en'ezet & St'ephane Cr'epey, 2022. "Hedging Valuation Adjustment and Model Risk," Papers 2205.11834, arXiv.org, revised Dec 2023.
    15. Dorinel Bastide & St'ephane Cr'epey, 2024. "Provisions and Economic Capital for Credit Losses," Papers 2401.07728, arXiv.org, revised Jan 2024.
    16. Dorinel Bastide & St'ephane Cr'epey & Samuel Drapeau & Mekonnen Tadese, 2022. "Derivatives Risks as Costs in a One-Period Network Model," Papers 2202.03248, arXiv.org, revised Feb 2022.
    17. Lokman A Abbas-Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA Regressions With Oversimulated Defaults," Post-Print hal-03910149, HAL.
    18. Lokman Abbas-Turki & St'ephane Cr'epey & Botao Li & Bouazza Saadeddine, 2024. "An Explicit Scheme for Pathwise XVA Computations," Papers 2401.13314, arXiv.org.
    19. Chaofan Sun & Ken Seng Tan & Wei Wei, 2022. "Credit Valuation Adjustment with Replacement Closeout: Theory and Algorithms," Papers 2201.09105, arXiv.org, revised Jan 2022.
    20. Narayan Ganesan & Bernhard Hientzsch, 2021. "Estimating Future VaR from Value Samples and Applications to Future Initial Margin," Papers 2104.11768, arXiv.org.
    21. Dorinel Bastide & Stéphane Crépey & Samuel Drapeau & Mekonnen Tadese, 2022. "Derivatives Risks as Costs in a One-Period Network Model," Post-Print hal-03910144, HAL.

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