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Capturing the intrinsic uncertainty of the VaR: Spectrum representation of a saddlepoint approximation for an estimator of the VaR

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Abstract

Though risk measurement is the core of most regulatory document, in both financial and insurance industries, risk managers and regulators pay little attention to the random behaviour of risk measures. To address this uncertainty, we provide a novel way to build a robust parametric confidence interval (CI) of Value-at-Risk (VaR) for different lengths of samples. We compute this CI from a saddlepoint approximation of the distribution of an estimator of VaR. Based on the CI, we create a spectrum representation that represents an area that we use to define a risk measure. We apply this methodology to risk management and stress testing providing an indicator of threats caused by events uncaptured in the traditional VaR methodology which can lead to dramatic failures

Suggested Citation

  • Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "Capturing the intrinsic uncertainty of the VaR: Spectrum representation of a saddlepoint approximation for an estimator of the VaR," Documents de travail du Centre d'Economie de la Sorbonne 16034r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2016.
  • Handle: RePEc:mse:cesdoc:16034r
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    References listed on IDEAS

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    1. Dominique Gu�gan & Bertrand Hassani & Kehan Li, 2015. "The Spectral Stress VaR (SSVaR)," Working Papers 2015:17, Department of Economics, University of Venice "Ca' Foscari".
    2. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2015. "The Spectral Stress VaR (SSVaR)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01169537, HAL.
    3. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    4. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer;Western Finance Association, vol. 12(2), pages 201-242, October.
    5. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2015. "The Spectral Stress VaR (SSVaR)," Documents de travail du Centre d'Economie de la Sorbonne 15052, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2015. "The Spectral Stress VaR (SSVaR)," Post-Print halshs-01169537, HAL.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Financial regulation; Value-at-Risk; Order statistic; Uncertainty; Saddlepoint approximation; Stress testing;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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