Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations

Noureddine Lehdili (), Pascal Oswald and Othmane Mirinioui
Additional contact information
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

Mathematics, 2024, vol. 12, issue 23, 1-27

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.

Keywords: credit valuation adjustment; expected exposure; Basel III; FRTB; potential future exposure; Gaussian process regression; machine learning; interest rate swaps (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/23/3779/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/23/3779/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:23:p:3779-:d:1533350

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().