Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations
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 Fundame...
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MDPI AG
2024-11-01
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| Series: | Mathematics |
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| author | Noureddine Lehdili Pascal Oswald Othmane Mirinioui |
| author_facet | Noureddine Lehdili Pascal Oswald Othmane Mirinioui |
| author_sort | Noureddine Lehdili |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-23c08122cc2e4797b7f59d07e771feae |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-23c08122cc2e4797b7f59d07e771feae2024-12-13T16:27:43ZengMDPI AGMathematics2227-73902024-11-011223377910.3390/math12233779Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment CalculationsNoureddine Lehdili0Pascal Oswald1Othmane Mirinioui2Market and Counterparty Risk Modeling (MCRM), Enterprise Risk Management Department (ERM), Natixis CIB, 75013 Paris, FranceMarket and Counterparty Risk Modeling (MCRM), Enterprise Risk Management Department (ERM), Natixis CIB, 75013 Paris, FranceMarket and Counterparty Risk Modeling (MCRM), Enterprise Risk Management Department (ERM), Natixis CIB, 75013 Paris, FranceCounterparty 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.https://www.mdpi.com/2227-7390/12/23/3779credit valuation adjustmentexpected exposureBasel IIIFRTBpotential future exposureGaussian process regression |
| spellingShingle | Noureddine Lehdili Pascal Oswald Othmane Mirinioui Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations Mathematics credit valuation adjustment expected exposure Basel III FRTB potential future exposure Gaussian process regression |
| title | Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations |
| title_full | Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations |
| title_fullStr | Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations |
| title_full_unstemmed | Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations |
| title_short | Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations |
| title_sort | leveraging bayesian quadrature for accurate and fast credit valuation adjustment calculations |
| topic | credit valuation adjustment expected exposure Basel III FRTB potential future exposure Gaussian process regression |
| url | https://www.mdpi.com/2227-7390/12/23/3779 |
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