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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
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    References listed on IDEAS

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    1. 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.
    2. 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.).
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    4. 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.
    5. 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.
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