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Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations

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  • St'ephane Cr'epey
  • Matthew Dixon

Abstract

Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for OTC derivative portfolio valuation involved in CVA computation. Our approach avoids nested simulation or simulation and regression of cash flows by learning a Gaussian metamodel for the mark-to-market cube of a derivative portfolio. We model the joint posterior of the derivatives as a Gaussian process over function space, with the spatial covariance structure imposed on the risk factors. Monte-Carlo simulation is then used to simulate the dynamics of the risk factors. The uncertainty in portfolio valuation arising from the Gaussian process approximation is quantified numerically. Numerical experiments demonstrate the accuracy and convergence properties of our approach for CVA computations, including a counterparty portfolio of interest rate swaps.

Suggested Citation

  • St'ephane Cr'epey & Matthew Dixon, 2019. "Gaussian Process Regression for Derivative Portfolio Modeling and Application to CVA Computations," Papers 1901.11081, arXiv.org, revised Oct 2019.
    • Handle: RePEc:arx:papers:1901.11081
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    References listed on IDEAS

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    1. Cousin, Areski & Maatouk, Hassan & Rullière, Didier, 2016. "Kriging of financial term-structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 631-648.
    2. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    3. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    4. 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.
    5. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    6. Marcelo Rosário da Barrosa & Arthur Valle Salles & Celma de Oliveira Ribeiro, 2016. "Portfolio optimization through Kriging methods," Applied Economics, Taylor & Francis Journals, vol. 48(50), pages 4894-4905, October.
    7. Chris Kenyon & Andrew Green, 2014. "Efficient XVA Management: Pricing, Hedging, and Attribution using Trade-Level Regression and Global Conditioning," Papers 1412.5332, arXiv.org, revised Dec 2014.
    8. 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.
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    Cited by:

    1. Hainaut, Donatien & Vrins, Frédéric, 2024. "European option pricing with model constrained Gaussian process regressions," LIDAM Discussion Papers ISBA 2024021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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