Quotation Fissler, Tobias. 2019. Elicitability of Range Value at Risk. Vienna Congress on Mathematical Finance, Wien, Österreich, 09.09.-11.09.


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Abstract

The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring function should be (strictly) consistent for the functional of interest, that is, the expected score should be minimised by the correctly specified functional value. A functional is elicitable if it possesses a strictly consistent scoring function. In quantitative risk management, the elicitability of a risk measure is closely related to comparative backtesting procedures. As such, it has gained considerable interest in the debate about which risk measure to choose in practice. While this discussion has mainly focused on the dichotomy between Value at Risk (VaR) – a quantile – and Expected Shortfall (ES) – a tail expectation, this talk is concerned with Range Value at Risk (RVaR). RVaR can be regarded as an interpolation of VaR and ES, which constitutes a tradeoff between the sensitivity of the latter and the robustness of the former. Recalling that RVaR is not elicitable, we show that a triplet of RVaR with two VaR components at different levels is elicitable. We characterise the class of strictly consistent scoring functions. Moreover, additional properties of these scoring functions are examined, including the diagnostic tool of Murphy diagrams. The results are illustrated with a simulation study, and we put our approach in perspective with respect to the classical approach of trimmed least squares in robust regression. This talk is based on joined work with Johanna F. Ziegel (preprint available at arXiv:1902.04489v2).

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Status of publication Published
Affiliation External
Type of publication Paper presented at an academic conference or symposium
Language English
Title Elicitability of Range Value at Risk.
Event Vienna Congress on Mathematical Finance
Year 2019
Date 09.09.-11.09.
Country Austria
Location Wien
URL https://fam.tuwien.ac.at/events/vcmf2019/

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Fissler, Tobias (Details)
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