Mitic, Peter;
(2024)
A Credibility Framework for Extreme Value-at-Risk.
Mathematics and Computer Science
, 18
, Article 6. 10.1007/s11786-024-00579-w.
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Abstract
Value-at-risk estimates derived from extreme value data by fitting fat-tailed distributions can be so large that their validity is open to question. In this paper, an objective criterion, and a framework from which it was developed, are presented in order to decide whether or not a fitted distribution is inappropriate for the purpose of value-at-risk calculation. That criterion is based on established extreme value theory (principally the Pickands-Balkema-deHaan Theorem), which is used to calculate a sequence of reference value-at-risk estimates using Generalised Pareto distributions. Those estimates are used to develop a closed-form formula for calculating a theoretical ’maximum’ value-at-risk. The method is validated by generating 100 random data sets and testing them against the framework for varying input parameter values. Approximately 75% of those cases passed the validation test.
| Type: | Article |
|---|---|
| Title: | A Credibility Framework for Extreme Value-at-Risk |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11786-024-00579-w |
| Publisher version: | https://doi.org/10.1007/s11786-024-00579-w |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Value at risk, Generalised Pareto, Gauss surface curvature, Mean surface curvature, Pareto–Pickands, Extreme value distributions, GPD-surface |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10189238 |
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