Estimation of tail risk based on extreme expectiles
We use tail expectiles to estimate alternative measures to the Value at Risk (VaR) and Marginal Expected Shortfall (MES), two instruments of risk protection of utmost importance in actuarial science and statistical _nance. The concept of expectiles is a least squares analogue of quantiles. Both are...
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| Format: | Article |
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Wiley
2017
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| Online Access: | https://eprints.nottingham.ac.uk/44962/ |
| _version_ | 1848797039245131776 |
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| author | Daouia, Abdelaati Girard, Stéphane Stupfler, Gilles |
| author_facet | Daouia, Abdelaati Girard, Stéphane Stupfler, Gilles |
| author_sort | Daouia, Abdelaati |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We use tail expectiles to estimate alternative measures to the Value at Risk (VaR) and Marginal Expected Shortfall (MES), two instruments of risk protection of utmost importance in actuarial science and statistical _nance. The concept of expectiles is a least squares analogue of quantiles. Both are M-quantiles as the minimizers of an asymmetric convex loss function, but expectiles are the only M-quantiles that are coherent risk measures. Moreover, expectiles de_ne the only coherent risk measure that is also elicitable. The estimation of expectiles has not, however, received any attention yet from the perspective of extreme values. Two estimation methods are proposed here, either making use of quantiles or relying directly on least asymmetrically weighted squares. A main tool is to _rst estimate large values of expectile-based VaR and MES located within the range of the data, and then to extrapolate the obtained estimates to the very far tails. We establish the limit distributions of both of the resulting intermediate and extreme estimators. We show via a detailed simulation study the good performance of the procedures, and present concrete applications to medical insurance data and three large US investment banks. |
| first_indexed | 2025-11-14T19:57:32Z |
| format | Article |
| id | nottingham-44962 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:57:32Z |
| publishDate | 2017 |
| publisher | Wiley |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-449622020-05-04T19:12:03Z https://eprints.nottingham.ac.uk/44962/ Estimation of tail risk based on extreme expectiles Daouia, Abdelaati Girard, Stéphane Stupfler, Gilles We use tail expectiles to estimate alternative measures to the Value at Risk (VaR) and Marginal Expected Shortfall (MES), two instruments of risk protection of utmost importance in actuarial science and statistical _nance. The concept of expectiles is a least squares analogue of quantiles. Both are M-quantiles as the minimizers of an asymmetric convex loss function, but expectiles are the only M-quantiles that are coherent risk measures. Moreover, expectiles de_ne the only coherent risk measure that is also elicitable. The estimation of expectiles has not, however, received any attention yet from the perspective of extreme values. Two estimation methods are proposed here, either making use of quantiles or relying directly on least asymmetrically weighted squares. A main tool is to _rst estimate large values of expectile-based VaR and MES located within the range of the data, and then to extrapolate the obtained estimates to the very far tails. We establish the limit distributions of both of the resulting intermediate and extreme estimators. We show via a detailed simulation study the good performance of the procedures, and present concrete applications to medical insurance data and three large US investment banks. Wiley 2017-10-10 Article PeerReviewed Daouia, Abdelaati, Girard, Stéphane and Stupfler, Gilles (2017) Estimation of tail risk based on extreme expectiles. Journal of the Royal Statistical Society: Series B, 80 (2). pp. 263-292. ISSN 1467-9868 Asymmetric squared loss; Coherency; Expectiles; Extrapolation; Extreme values; Heavy tails; Marginal expected shortfall; Value at Risk http://onlinelibrary.wiley.com/doi/10.1111/rssb.12254/full doi:10.1111/rssb.12254 doi:10.1111/rssb.12254 |
| spellingShingle | Asymmetric squared loss; Coherency; Expectiles; Extrapolation; Extreme values; Heavy tails; Marginal expected shortfall; Value at Risk Daouia, Abdelaati Girard, Stéphane Stupfler, Gilles Estimation of tail risk based on extreme expectiles |
| title | Estimation of tail risk based on extreme expectiles |
| title_full | Estimation of tail risk based on extreme expectiles |
| title_fullStr | Estimation of tail risk based on extreme expectiles |
| title_full_unstemmed | Estimation of tail risk based on extreme expectiles |
| title_short | Estimation of tail risk based on extreme expectiles |
| title_sort | estimation of tail risk based on extreme expectiles |
| topic | Asymmetric squared loss; Coherency; Expectiles; Extrapolation; Extreme values; Heavy tails; Marginal expected shortfall; Value at Risk |
| url | https://eprints.nottingham.ac.uk/44962/ https://eprints.nottingham.ac.uk/44962/ https://eprints.nottingham.ac.uk/44962/ |