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Limit Theory for Forecasts of Extreme Distortion Risk Measures and Expectiles
[Coherent Measures of Risk]

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  • Yannick Hoga

Abstract

We develop central limit theory for tail risk forecasts in general location–scale models. We do so for a wide range of risk measures, viz. distortion risk measures (DRMs) and expectiles. Two popular members of the class of DRMs are the Value-at-Risk and the Expected Shortfall. The forecasts we consider are motivated by a Pareto-type tail assumption for the innovations and allow for extrapolation beyond the range of available observations. Simulations reveal adequate coverage of the forecast intervals derived from the limit theory. An empirical application demonstrates that our estimators outperform nonparametric alternatives when forecasting extreme risk in sufficiently large samples.

Suggested Citation

  • Yannick Hoga, 2022. "Limit Theory for Forecasts of Extreme Distortion Risk Measures and Expectiles [Coherent Measures of Risk]," Journal of Financial Econometrics, Oxford University Press, vol. 20(1), pages 18-44.
    • Handle: RePEc:oup:jfinec:v:20:y:2022:i:1:p:18-44.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbz032
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    Cited by:

    1. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.

    More about this item

    Keywords

    central limit theory; distortion risk measures; expectiles; extreme value theory; location–scale model;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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