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XVA analysis from the balance sheet

Author

Listed:
  • Claudio Albanese
  • Stéphane Crépey
  • Rodney Hoskinson
  • Bouazza Saadeddine

Abstract

XVAs denote various counterparty risk related valuation adjustments that are applied to financial derivatives since the 2007–2009 crisis. We root a cost-of-capital XVA strategy in a balance sheet perspective which is key to 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 into the dynamic and trade incremental context of a real derivative banking portfolio. The corresponding cost-of-capital XVA strategy ensures for 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 & Stéphane Crépey & Rodney Hoskinson & Bouazza Saadeddine, 2021. "XVA analysis from the balance sheet," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 99-123, January.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:1:p:99-123
    DOI: 10.1080/14697688.2020.1817533
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    1. Leif Andersen & Darrell Duffie & Yang Song, 2019. "Funding Value Adjustments," Journal of Finance, American Finance Association, vol. 74(1), pages 145-192, February.
    2. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
    3. Gottardi, Piero, 1995. "An Analysis of the Conditions for the Validity of Modigliani-Miller Theorem with Incomplete Markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 191-207, March.
    4. Stéphane Crépey & Wissal Sabbagh & Shiqi Song, 2020. "When Capital Is a Funding Source: The Anticipated Backward Stochastic Differential Equations of X-Value Adjustments," Post-Print hal-03910119, HAL.
    5. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    6. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    7. Lokman A. Abbas-Turki & Stéphane Crépey & Babacar Diallo, 2018. "Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-40, September.
    8. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
    9. Youssef Elouerkhaoui, 2007. "Pricing And Hedging In A Dynamic Credit Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 703-731.
    10. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    11. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    12. Stéphane Crépey & Shiqi Song, 2017. "Invariance Times ," Working Papers hal-01455414, HAL.
    13. Youssef Elouerkhaoui, 2007. "Pricing And Hedging In A Dynamic Credit Model," World Scientific Book Chapters, in: Alexander Lipton & Andrew Rennie (ed.), Credit Correlation Life After Copulas, chapter 6, pages 111-139, World Scientific Publishing Co. Pte. Ltd..
    14. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
    15. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.
    16. Duffie, Darrell & Huang, Ming, 1996. "Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
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    Citations

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    Cited by:

    1. Giorgia Callegaro & Alessandro Gnoatto & Martino Grasselli, 2021. "A Fully Quantization-based Scheme for FBSDEs," Working Papers 07/2021, University of Verona, Department of Economics.
    2. Cyril B'en'ezet & St'ephane Cr'epey, 2022. "Handling model risk with XVAs," Papers 2205.11834, arXiv.org, revised Aug 2024.
    3. Lokman A Abbas-Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA Regressions With Oversimulated Defaults," Post-Print hal-03910149, HAL.
    4. St'ephane Cr'epey & Botao Li & Hoang Nguyen & Bouazza Saadeddine, 2024. "CVA Sensitivities, Hedging and Risk," Papers 2407.18583, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Lokman Abbas-Turki & St'ephane Cr'epey & Botao Li & Bouazza Saadeddine, 2024. "An Explicit Scheme for Pathwise XVA Computations," Papers 2401.13314, arXiv.org.
    10. Dorinel Bastide & Stéphane Crépey & Samuel Drapeau & Mekonnen Tadese, 2022. "Derivatives Risks as Costs in a One-Period Network Model," Post-Print hal-03910144, HAL.
    11. Joel P. Villarino & 'Alvaro Leitao, 2024. "On Deep Learning for computing the Dynamic Initial Margin and Margin Value Adjustment," Papers 2407.16435, arXiv.org.
    12. 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.
    13. Dorinel Bastide & Stéphane Crépey & Samuel Drapeau & Mekonnen Tadese, 2022. "Derivatives Risks as Costs in a One-Period Network Model," Working Papers hal-03554577, HAL.
    14. 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.
    15. 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.
    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. Narayan Ganesan & Bernhard Hientzsch, 2021. "Estimating Future VaR from Value Samples and Applications to Future Initial Margin," Papers 2104.11768, arXiv.org.
    18. D Barrera & S Cr'epey & E Gobet & Hoang-Dung Nguyen & B Saadeddine, 2022. "Statistical Learning of Value-at-Risk and Expected Shortfall," Papers 2209.06476, arXiv.org, revised Sep 2024.
    19. Callegaro, Giorgia & Gnoatto, Alessandro & Grasselli, Martino, 2023. "A fully quantization-based scheme for FBSDEs," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    20. Stéphane Crépey, 2022. "Positive XVAs," Post-Print hal-03910135, HAL.
    21. D Barrera & S Crépey & E Gobet & Hoang-Dung Nguyen & B Saadeddine, 2022. "Learning Value-at-Risk and Expected Shortfall," Working Papers hal-03775901, HAL.
    22. Lokman Abbas-Turki & St'ephane Cr'epey & Bouazza Saadeddine, 2022. "Pathwise CVA Regressions With Oversimulated Defaults," Papers 2211.17005, arXiv.org.
    23. Dorinel Bastide & St'ephane Cr'epey, 2024. "Provisions and Economic Capital for Credit Losses," Papers 2401.07728, arXiv.org, revised Jan 2024.

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