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Model-Free Inference For Tail Risk Measures

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  • Xu, Ke-Li

Abstract

Understanding uncertainty in estimating risk measures is important in modern financial risk management. In this paper we consider a nonparametric framework that incorporates auxiliary information available in covariates and propose a family of inferential methods for the value at risk, expected shortfall, and related risk measures. A two-step generalized empirical likelihood test statistic is constructed and is shown to be asymptotically pivotal without requiring variance estimation. We also show its validity when applied to a semiparametric index model. Asymptotic theories are established allowing for serially dependent data. Simulations and an empirical application to Canadian stock return index illustrate the finite sample behavior of the methodologies proposed.

Suggested Citation

  • Xu, Ke-Li, 2016. "Model-Free Inference For Tail Risk Measures," Econometric Theory, Cambridge University Press, vol. 32(1), pages 122-153, February.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:01:p:122-153_00
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    Cited by:

    1. Lin Fan & Peter W. Glynn & Markus Pelger, 2018. "Change-Point Testing for Risk Measures in Time Series," Papers 1809.02303, arXiv.org, revised Jul 2023.
    2. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    3. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.

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