Quotation Fissler, Tobias, Ziegel, Johanna F. 2021. On the elicitability of range value at risk. Statistics and Risk Modeling. 38 (1-2), 25-46.


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Abstract

The debate of which quantitative risk measure to choose in practice has mainly focused on the dichotomy between value at risk (VaR) and expected shortfall (ES). Range value at risk (RVaR) is a natural interpolation between VaR and ES, constituting a tradeoff between the sensitivity of ES and the robustness of VaR, turning it into a practically relevant risk measure on its own. Hence, there is a need to statistically assess, compare and rank the predictive performance of different RVaR models, tasks subsumed under the term “comparative backtesting” in finance. This is best done in terms of strictly consistent loss or scoring functions, i.e., functions which are minimized in expectation by the correct risk measure forecast. Much like ES, RVaR does not admit strictly consistent scoring functions, i.e., it is not elicitable. Mitigating this negative result, we show that a triplet of RVaR with two VaR-components is elicitable. We characterize all strictly consistent scoring functions for this triplet. 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 regression.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Statistics and Risk Modeling
WU-Journal-Rating new FIN-A, VW-C
Language English
Title On the elicitability of range value at risk
Volume 38
Number 1-2
Year 2021
Page from 25
Page to 46
Reviewed? Y
URL https://www.degruyter.com/document/doi/10.1515/strm-2020-0037/xml
DOI http://dx.doi.org/10.1515/strm-2020-0037
Open Access Y
Open Access Link https://doi.org/10.1515/strm-2020-0037
JEL MSC 2010: 62C99; 62G35; 62P05; 91G70

Associations

People
Fissler, Tobias (Details)
External
Ziegel, Johanna F. (University of Bern, Switzerland)
Organization
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1113 Mathematical statistics (Details)
1117 Actuarial mathematics (Details)
1137 Financial mathematics (Details)
1162 Statistics (Details)
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