Corrected inference about the extreme Expected Shortfall in the general max-domain of attraction

Abdelaati Daouia, Gilles Stupfler and Antoine Usseglio-Carleve

No 24-1565, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: The use of the Expected Shortfall as a solution for various deficiencies of quantiles has gained substantial traction in the field of risk assessment over the last 20 years. Existing approaches to its inference at extreme levels remain limited to distributions that are both heavy-tailed and have a finite second tail moment. This constitutes a strong restriction in areas like finance and environmental science, where the random variable of interest may have a much heavier tail or, at the opposite, may be light-tailed or short-tailed. Under a wider semiparametric extreme value framework, we develop comprehensive asymptotic theory for Expected Shortfall estimation above extreme quantiles in the class of distributions with finite first tail moment, regardless of whether the underlying extreme value index is positive, negative, or zero. By relying on the moment estimators of the scale and shape extreme value parameters, we construct corrected asymptotic confidence intervals whose finite-sample coverage is found to be close to the nominal level on simulated data. We illustrate the usefulness of our construction on two sets of financial loss returns and flood insurance claims data.

Keywords: Expected Shortfall, extreme value moment estimator, inference, second-order; extended regular variation, semiparametric extrapolation. (search for similar items in EconPapers)
Date: 2024, Revised 2024-12
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.tse-fr.eu/sites/default/files/TSE/docu ... 2024/wp_tse_1565.pdf Working Paper (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:129693

Access Statistics for this paper

More papers in TSE Working Papers from Toulouse School of Economics (TSE) Contact information at EDIRC.
Bibliographic data for series maintained by ().