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Deep xVA solver -- A neural network based counterparty credit risk management framework

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  • Alessandro Gnoatto
  • Athena Picarelli
  • Christoph Reisinger

Abstract

In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method utilises a coupled system of BSDEs for the valuation adjustments (xVA) and solves these by a recursive application of a neural network based BSDE solver. This not only makes the computation of xVA for high-dimensional problems feasible, but also produces hedge ratios and dynamic risk measures for xVA, and allows simulations of the collateral account.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2005.02633
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    1. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," Papers 1710.07030, arXiv.org, revised Mar 2019.
    2. 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.
    3. Leif Andersen & Darrell Duffie & Yang Song, 2019. "Funding Value Adjustments," Journal of Finance, American Finance Association, vol. 74(1), pages 145-192, February.
    4. Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Arbitrage-Free Valuation Of Bilateral Counterparty Risk For Interest-Rate Products: Impact Of Volatilities And Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 773-802.
    5. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
    6. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    7. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2018. "Risk-neutral valuation under differential funding costs, defaults and collateralization," Papers 1802.10228, arXiv.org.
    8. Francesca Biagini & Alessandro Gnoatto & Immacolata Oliva, 2019. "Pricing of counterparty risk and funding with CSA discounting, portfolio effects and initial margin," Working Papers 04/2019, University of Verona, Department of Economics.
    9. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    10. 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.
    11. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Market Model of Interest Rates with Dynamic Basis Spreads in the presence of Collateral and Multiple Currencies," CARF F-Series CARF-F-196, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Apr 2011.
    12. Alessandro Gnoatto & Nicole Seiffert, 2020. "Cross Currency Valuation and Hedging in the Multiple Curve Framework," Working Papers 03/2020, University of Verona, Department of Economics.
    13. Christian P. Fries, 2019. "Stochastic automatic differentiation: automatic differentiation for Monte-Carlo simulations," Quantitative Finance, Taylor & Francis Journals, vol. 19(6), pages 1043-1059, June.
    14. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    15. Ryan Ferguson & Andrew Green, 2018. "Deeply Learning Derivatives," Papers 1809.02233, arXiv.org, revised Oct 2018.
    16. Syoiti Ninomiya & Yuji Shinozaki, 2019. "Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(3), pages 257-292, May.
    17. Mark Joshi & Oh Kang Kwon, 2016. "Least Squares Monte Carlo Credit Value Adjustment With Small And Unidirectional Bias," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-16, December.
    18. Patrik Karlsson & Shashi Jain & Cornelis W. Oosterlee, 2016. "Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(3), pages 175-196, May.
    19. Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197, arXiv.org, revised Feb 2018.
    20. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-456, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    21. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2011. "Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation," Papers 1112.1521, arXiv.org, revised Dec 2011.
    22. Brigo, Damiano & Francischello, Marco & Pallavicini, Andrea, 2019. "Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement," European Journal of Operational Research, Elsevier, vol. 274(2), pages 788-805.
    23. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    24. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 391-408, September.
    25. 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.
    26. Duffie, Darrell & Huang, Ming, 1996. "Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-949, July.
    27. Cornelis S. L. De Graaf & Qian Feng & Drona Kandhai & Cornelis W. Oosterlee, 2014. "Efficient Computation Of Exposure Profiles For Counterparty Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-23.
    28. C. S. L. de Graaf & D. Kandhai & C. Reisinger, 2018. "Efficient exposure computation by risk factor decomposition," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1657-1678, October.
    29. 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.
    30. Masaaki Fujii & Yasufumi Shimada & Akihiko Takahashi, 2009. "A Note on Construction of Multiple Swap Curves with and without Collateral," CARF F-Series CARF-F-154, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2010.
    31. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
    32. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Griselda Deelstra & Lech A. Grzelak & Felix L. Wolf, 2022. "Accelerated Computations of Sensitivities for xVA," Papers 2211.17026, arXiv.org, revised Jan 2024.
    2. Giorgia Callegaro & Alessandro Gnoatto & Martino Grasselli, 2021. "A Fully Quantization-based Scheme for FBSDEs," Working Papers 07/2021, University of Verona, Department of Economics.
    3. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," CARF F-Series CARF-F-504, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2022.
    4. 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.
    5. Takayuki Sakuma, 2020. "Application of deep quantum neural networks to finance," Papers 2011.07319, arXiv.org, revised May 2022.
    6. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A New Efficient Approximation Scheme for Solving High-Dimensional Semilinear PDEs: Control Variate Method for Deep BSDE Solver," CIRJE F-Series CIRJE-F-1159, CIRJE, Faculty of Economics, University of Tokyo.
    7. Joel P. Villarino & 'Alvaro Leitao & Jos'e A. Garc'ia-Rodr'iguez, 2022. "Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk," Papers 2210.02175, arXiv.org.
    8. Lokman Abbas-Turki & St'ephane Cr'epey & Bouazza Saadeddine, 2022. "Pathwise CVA Regressions With Oversimulated Defaults," Papers 2211.17005, arXiv.org.
    9. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2022. "Computing XVA for American basket derivatives by Machine Learning techniques," Papers 2209.06485, arXiv.org.
    10. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2022. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver (Journal of Computational Physics, published online 19 January 2022)," CARF F-Series CARF-F-532, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2022.
    11. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," Papers 2101.09890, arXiv.org, revised Jan 2021.
    12. Lokman A Abbas-Turki & Stéphane Crépey & Bouazza Saadeddine, 2023. "Pathwise CVA Regressions With Oversimulated Defaults," Post-Print hal-03910149, HAL.
    13. Chaofan Sun & Ken Seng Tan & Wei Wei, 2022. "Credit Valuation Adjustment with Replacement Closeout: Theory and Algorithms," Papers 2201.09105, arXiv.org, revised Jan 2022.
    14. Elisa Al`os & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2022. "CVA in fractional and rough volatility models," Papers 2204.11554, arXiv.org.

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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