IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3779-d1533350.html
   My bibliography  Save this article

Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations

Author

Listed:
  • Noureddine Lehdili

    (Market and Counterparty Risk Modeling (MCRM), Enterprise Risk Management Department (ERM), Natixis CIB, 75013 Paris, France)

  • Pascal Oswald

    (Market and Counterparty Risk Modeling (MCRM), Enterprise Risk Management Department (ERM), Natixis CIB, 75013 Paris, France)

  • Othmane Mirinioui

    (Market and Counterparty Risk Modeling (MCRM), Enterprise Risk Management Department (ERM), Natixis CIB, 75013 Paris, France)

Abstract

Counterparty risk, which combines market and credit risks, gained prominence after the 2008 financial crisis due to its complexity and systemic implications. Traditional management methods, such as netting and collateralization, have become computationally demanding under frameworks like the Fundamental Review of the Trading Book (FRTB). This paper explores the combined application of Gaussian process regression (GPR) and Bayesian quadrature (BQ) to enhance the efficiency and accuracy of counterparty risk metrics, particularly credit valuation adjustment (CVA). This approach balances excellent precision with significant computational performance gains. Focusing on fixed-income derivatives portfolios, such as interest rate swaps and swaptions, within the One-Factor Linear Gaussian Markov (LGM-1F) model framework, we highlight three key contributions. First, we approximate swaption prices using Bachelier’s formula, showing that forward-starting swap rates can be modeled as Gaussian dynamics, enabling efficient CVA computations. Second, we demonstrate the practical relevance of an analytical approximation for the CVA of an interest rate swap portfolio. Finally, the combined use of Gaussian processes and Bayesian quadrature underscores a powerful synergy between precision and computational efficiency, making it a valuable tool for credit risk management.

Suggested Citation

  • Noureddine Lehdili & Pascal Oswald & Othmane Mirinioui, 2024. "Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations," Mathematics, MDPI, vol. 12(23), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3779-:d:1533350
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3779/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3779/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Martin Leo & Suneel Sharma & K. Maddulety, 2019. "Machine Learning in Banking Risk Management: A Literature Review," Risks, MDPI, vol. 7(1), pages 1-22, March.
    2. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    3. Wilkens, Sascha, 2019. "Machine learning in risk measurement: Gaussian process regression for value-at-risk and expected shortfall," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 12(4), pages 374-383, September.
    4. Michael Pykhtin & Dan Rosen, 2010. "Pricing counterparty risk at the trade level and CVA allocations," Finance and Economics Discussion Series 2010-10, Board of Governors of the Federal Reserve System (U.S.).
    5. Qian Liu, 2015. "Calculation of Credit Valuation Adjustment Based on Least Square Monte Carlo Methods," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-6, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bauer, Kevin & Nofer, Michael & Abdel-Karim, Benjamin M. & Hinz, Oliver, 2022. "The effects of discontinuing machine learning decision support," SAFE Working Paper Series 370, Leibniz Institute for Financial Research SAFE.
    2. John R. J. Thompson & Longlong Feng & R. Mark Reesor & Chuck Grace, 2021. "Know Your Clients’ Behaviours: A Cluster Analysis of Financial Transactions," JRFM, MDPI, vol. 14(2), pages 1-29, January.
    3. Sina Montazeri & Akram Mirzaeinia & Haseebullah Jumakhan & Amir Mirzaeinia, 2024. "CNN-DRL for Scalable Actions in Finance," Papers 2401.06179, arXiv.org.
    4. Kim, Jong-Min & Kim, Dong H. & Jung, Hojin, 2021. "Applications of machine learning for corporate bond yield spread forecasting," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    5. Polyzos, Stathis & Samitas, Aristeidis & Katsaiti, Marina-Selini, 2020. "Who is unhappy for Brexit? A machine-learning, agent-based study on financial instability," International Review of Financial Analysis, Elsevier, vol. 72(C).
    6. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    7. Gero Junike & Hauke Stier, 2024. "Enhancing Fourier pricing with machine learning," Papers 2412.05070, arXiv.org.
    8. Keerthana Sivamayil & Elakkiya Rajasekar & Belqasem Aljafari & Srete Nikolovski & Subramaniyaswamy Vairavasundaram & Indragandhi Vairavasundaram, 2023. "A Systematic Study on Reinforcement Learning Based Applications," Energies, MDPI, vol. 16(3), pages 1-23, February.
    9. Pejman Peykani & Mostafa Sargolzaei & Mohammad Hashem Botshekan & Camelia Oprean-Stan & Amir Takaloo, 2023. "Optimization of Asset and Liability Management of Banks with Minimum Possible Changes," Mathematics, MDPI, vol. 11(12), pages 1-24, June.
    10. Dmytro Kovalenko & Olga Afanasieva & Nani Zabuta & Tetiana Boiko & Rosen Rosenov Baltov, 2021. "Model of Assessing the Overdue Debts in a Commercial Bank Using Neuro-Fuzzy Technologies," JRFM, MDPI, vol. 14(5), pages 1-20, May.
    11. Goudenège, Ludovic & Molent, Andrea & Zanette, Antonino, 2022. "Moving average options: Machine learning and Gauss-Hermite quadrature for a double non-Markovian problem," European Journal of Operational Research, Elsevier, vol. 303(2), pages 958-974.
    12. Sandrine Gumbel & Thorsten Schmidt, 2020. "Machine learning for multiple yield curve markets: fast calibration in the Gaussian affine framework," Papers 2004.07736, arXiv.org, revised Apr 2020.
    13. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2024. "Neural Networks for Portfolio-Level Risk Management: Portfolio Compression, Static Hedging, Counterparty Credit Risk Exposures and Impact on Capital Requirement," Papers 2402.17941, arXiv.org.
    14. Xu, Zhaoyi & Saleh, Joseph Homer, 2021. "Machine learning for reliability engineering and safety applications: Review of current status and future opportunities," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    15. Rubesam, Alexandre, 2022. "Machine learning portfolios with equal risk contributions: Evidence from the Brazilian market," Emerging Markets Review, Elsevier, vol. 51(PB).
    16. Fred Espen Benth & Nils Detering & Silvia Lavagnini, 2021. "Accuracy of deep learning in calibrating HJM forward curves," Digital Finance, Springer, vol. 3(3), pages 209-248, December.
    17. Damiano Brigo & Andrea Pallavicini, 2013. "CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?," Papers 1312.0128, arXiv.org, revised Dec 2013.
    18. Ni Zhan, 2021. "Where does the Stimulus go? Deep Generative Model for Commercial Banking Deposits," Papers 2101.09230, arXiv.org.
    19. Demiralay, Sercan & Gencer, Hatice Gaye & Bayraci, Selcuk, 2022. "Carbon credit futures as an emerging asset: Hedging, diversification and downside risks," Energy Economics, Elsevier, vol. 113(C).
    20. Naman Krishna Pande & Puneet Pasricha & Arun Kumar & Arvind Kumar Gupta, 2024. "European Option Pricing in Regime Switching Framework via Physics-Informed Residual Learning," Papers 2410.10474, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3779-:d:1533350. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.