COHERENCE AND ELICITABILITY

By J. Ziegel. 2013

359 citations recorded by the source corpus.

The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical decision theory, risk measures for which such verification and comparison is possible, are called elicitable. It is known that quantile‐based risk measures such as value at risk are elicitable. In this paper, the existing result of the nonelicitability of expected shortfall is extended to all law‐invariant spectral risk measures unless they reduce to minus the expected value. Hence, it is unclear how to perform forecast verification or comparison. However, the class of elicitable law‐invariant coherent risk measures does not reduce to minus the expected value. We show that it consists of certain expectiles.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/deeb7bae837abe42bf445a23368f8960b3f89f55

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In Finance

1. Paul Embrechts
2. J. Ziegel
3. St'ephane Cr'epey
4. Damiano Brigo
5. Ruodu Wang
6. James W. Taylor
7. Alexander J. McNeil
8. Natalia Nolde

In Management Science and Operations Research

1. Paul Embrechts
2. J. Ziegel
3. Ludger Rüschendorf
4. Ruodu Wang
5. Alexander J. McNeil
6. Chengguo Weng
7. Damiano Brigo
8. Natalia Nolde

Citations in the corpus

• Higher order elicitability and Osband’s principle (2015, background): “2006; Gneiting, 2011), whereas VaRα is 1-elicitable for most classes of distributions F of practial relevance. In fact, except for the expectation, all spectral risk measures fail to be 1-elicitable (Ziegel, 2015); further recent results on elicitable risk measures include (Kou and Peng, 2014; Wang ”
• Generalized Quantiles as Risk Measures (2014, background): “…for a functional that is defined by means of a similar loss minimization process; the relevance of elicitability in connection with backtesting has been recently addressed by Embrechts and Hofert (2013) while the relationship between coherency and elicitability has been considered in Ziegel (2013).”
• An Academic Response to Basel 3.5 (2014, background): “” Recently, considerable progress has been made concerning the embedding of the statistical theory of elicitability within the mathematical theory of risk measures; see for instance Ziegel (2014). An interesting question that early on emerged from this research was: “Do there exist (non-trivial) coh”
• Expectile Asymptotics (2015, background): “Indeed, expectiles were shown to be the only coherent, elicitable risk measures in Ziegel (2014); for a discussion and comparison between value at risk (quantiles), expectiles and expected shortfall see Emmer et al. (2015).”
• Counterparty Risk and Funding: A Tale of Two Puzzles (2014, background): “However, expected shortfall is not elicitable, as discussed in Ziegel (2013), whereas VaR is.”
• Estimation of tail risk based on extreme expectiles (2016, neutral): “It has been shown that the Expected Shortfall (ES), viewed as the most popular coherent risk measure, is not elicitable (Gneiting, 2011), but jointly elicitable with VaR (Fissler and Ziegel, 2016).”
• Forecasting risk with Markov-switching GARCH models:A large-scale performance study (2018, methodology): “Unfortunately, there is no loss function available for which the ES risk measure can be elicited; see for instance Bellini & Bignozzi (2015) and Ziegel (2016).”
• Multinomial VaR Backtests: A simple implicit approach to backtesting expected shortfall (2016, methodology): “Fissler & Ziegel (2016) show that VaR and ES are jointly elicitable in the sense that they jointly minimize an appropriate bi-dimensional scoring function; this allows the comparison of different forecasting methods that give estimates of both VaR and ES.”
• Optimal reinsurance with expectile (2016, background): “It is known that the VaR is elicitable, whereas the ES is not elicitable as shown by Ziegel (2014).”
• Elicitability and backtesting: Perspectives for banking regulation (2016, background): “Moreover, traditional backtests may not provide banks with the right incentive of developing procedures which aim for accuracy of risk measure forecasts; for an illustration, see Section A of the online supplement [Nolde and Ziegel, 2016] (abbreviated ’OS’ in the sequel).”