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Statistical Learning of Value-at-Risk and Expected Shortfall

Author

Listed:
  • D Barrera

    (UNIANDES)

  • S Cr'epey

    (LPSM)

  • E Gobet

    (CMAP, X)

  • Hoang-Dung Nguyen

    (LPSM)

  • B Saadeddine

    (UEVE)

Abstract

We propose a non-asymptotic convergence analysis of a two-step approach to learn a conditional value-at-risk (VaR) and a conditional expected shortfall (ES) using Rademacher bounds, in a non-parametric setup allowing for heavy-tails on the financial loss. Our approach for the VaR is extended to the problem of learning at once multiple VaRs corresponding to different quantile levels. This results in efficient learning schemes based on neural network quantile and least-squares regressions. An a posteriori Monte Carlo procedure is introduced to estimate distances to the ground-truth VaR and ES. This is illustrated by numerical experiments in a Student-$t$ toy model and a financial case study where the objective is to learn a dynamic initial margin.

Suggested Citation

  • D Barrera & S Cr'epey & E Gobet & Hoang-Dung Nguyen & B Saadeddine, 2022. "Statistical Learning of Value-at-Risk and Expected Shortfall," Papers 2209.06476, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2209.06476
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    File URL: http://arxiv.org/pdf/2209.06476
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    References listed on IDEAS

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    1. Roger Koenker, 2017. "Quantile Regression: 40 Years On," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 155-176, September.
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    3. Yufeng Liu & Yichao Wu, 2011. "Simultaneous multiple non-crossing quantile regression estimation using kernel constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 415-437.
    4. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    5. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    6. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. 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.
    8. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    9. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
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    Cited by:

    1. Weronika Ormaniec & Marcin Pitera & Sajad Safarveisi & Thorsten Schmidt, 2022. "Estimating value at risk: LSTM vs. GARCH," Papers 2207.10539, arXiv.org.

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