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Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations

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  • LOKMAN A. ABBAS-TURKI

    (Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre-et-Marie Curie, UMR 7599, France)

  • STÉPHANE CRÉPEY

    (#x2020;LaMME, Université d’Evry, CNRS, Université Paris-Saclay, 91037, Evry, France)

  • BABACAR DIALLO

    (Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre-et-Marie Curie, UMR 7599, France†LaMME, Université d’Evry, CNRS, Université Paris-Saclay, 91037, Evry, France‡Quantitative Research GMD/GMT Crédit Agricole, CIB 92160, Montrouge, France)

Abstract

We present a nested Monte Carlo (NMC) approach implemented on graphics processing units (GPUs) to X-valuation adjustments (XVAs), where X ranges over C for credit, F for funding, M for margin, and K for capital. The overall XVA suite involves five compound layers of dependence. Higher layers are launched first, and trigger nested simulations on-the-fly whenever required in order to compute an item from a lower layer. If the user is only interested in some of the XVA components, then only the sub-tree corresponding to the most outer XVA needs be processed computationally. Inner layers only need a square root number of simulation with respect to the most outer layer. Some of the layers exhibit a smaller variance. As a result, with GPUs at least, error-controlled NMC XVA computations are doable. But, although NMC is naively suited to parallelization, a GPU implementation of NMC XVA computations requires various optimizations. This is illustrated on XVA computations involving equities, interest rate, and credit derivatives, for both bilateral and central clearing XVA metrics.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:06:n:s0219024918500309
    DOI: 10.1142/S0219024918500309
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    References listed on IDEAS

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    1. L.A. Abbas-Turki & S. Vialle & Bernard Lapeyre & P. Mercier, 2014. "Pricing derivatives on graphics processing units using Monte Carlo simulation," Post-Print hal-01667067, HAL.
    2. Leif Andersen & Darrell Duffie & Yang Song, 2017. "Funding Value Adjustments," NBER Working Papers 23680, National Bureau of Economic Research, Inc.
    3. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    4. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
    5. Youssef Elouerkhaoui, 2007. "Pricing And Hedging In A Dynamic Credit Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 703-731.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    8. Youssef Elouerkhaoui, 2007. "Pricing And Hedging In A Dynamic Credit Model," World Scientific Book Chapters, in: Alexander Lipton & Andrew Rennie (ed.), Credit Correlation Life After Copulas, chapter 6, pages 111-139, World Scientific Publishing Co. Pte. Ltd..
    9. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    10. Moran, Lee & Wilkens, Sascha, 2017. "Capturing initial margin in counterparty risk calculations," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 10(2), pages 118-129, April.
    11. Claudio Albanese & Toufik Bellaj & Guillaume Gimonet & Giacomo Pietronero, 2011. "Coherent global market simulations and securitization measures for counterparty credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 11(1), pages 1-20.
    12. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.
    13. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    14. Whitney K. Newey, 1995. "Convergence Rates & Asymptotic Normality Estimators," Working papers 95-13, Massachusetts Institute of Technology (MIT), Department of Economics.
    15. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
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    Cited by:

    1. Lokman A Abbas-Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA Regressions With Oversimulated Defaults," Post-Print hal-03910149, HAL.
    2. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    3. Lokman Abbas-Turki & St'ephane Cr'epey & Botao Li & Bouazza Saadeddine, 2024. "An Explicit Scheme for Pathwise XVA Computations," Papers 2401.13314, arXiv.org.
    4. Stéphane Crépey & Matthew F Dixon, 2020. "Gaussian process regression for derivative portfolio modeling and application to credit valuation adjustment computations," Post-Print hal-03910109, HAL.
    5. 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.
    6. Claudio Albanese & Stéphane Crépey & Rodney Hoskinson & Bouazza Saadeddine, 2021. "XVA analysis from the balance sheet," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 99-123, January.
    7. Grzelak, Lech A., 2022. "Sparse grid method for highly efficient computation of exposures for xVA," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    8. Lokman A. Abbas‐Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA regressions with oversimulated defaults," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 274-307, April.
    9. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2021. "Stability of backward stochastic differential equations: the general case," Papers 2107.11048, arXiv.org, revised Apr 2023.
    10. Lech A. Grzelak, 2021. "Sparse Grid Method for Highly Efficient Computation of Exposures for xVA," Papers 2104.14319, arXiv.org, revised May 2022.
    11. Claudio Albanese & Marc Chataigner & Stéphane Crépey, 2020. "Wealth Transfers, Indifference Pricing, and XVA Compression Schemes," Post-Print hal-03910047, HAL.
    12. Lokman Abbas-Turki & St'ephane Cr'epey & Bouazza Saadeddine, 2022. "Pathwise CVA Regressions With Oversimulated Defaults," Papers 2211.17005, arXiv.org.

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