文章基本信息

标题：Value-at-Risk Estimation and the PORT Mean-of-order-p Methodology
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作者：Fernanda Figueiredo ; M. Ivette Gomes ; Lígia Henriques-Rodrigues. 等
期刊名称：RevStat : Statistical Journal
印刷版ISSN：1645-6726
出版年度：2017
卷号：15
期号：2
页码：187-204
出版社：Instituto Nacional de Estatística
摘要：In finance, insurance and statistical quality control, among many other areas of appli- cation, a typical requirement is to estimate the value-at-risk (VaR) at a small level q, i.e. a high quantile of probability 1 . q, a value, high enough, so that the chance of an exceedance of that value is equal to q, small. The semi-parametric estimation of high quantiles depends strongly on the estimation of the extreme value index (EVI), the primary parameter of extreme events. And most semi-parametric VaR-estimators do not enjoy the adequate behaviour, in the sense that they do not su.er the appropriate linear shift in the presence of linear transformations of the data. Recently, and for heavy tails, i.e. for a positive EVI, new VaR-estimators were intro duced with such a behaviour, the so-called PORT VaR-estimators, with PORT standing for peaks over a random threshold. Regarding EVI-estimation, new classes of PORT-EVI estimators, based on a powerful generalization of the Hill EVI-estimator related to adequate mean- of-order-p (MO p ) EVI-estimators, were even more recently intro duced. In this article, also for heavy tails, we intro duce a new class of PORT-MO p VaR-estimators with the above mentioned behaviour, using the PORT-MO p class of EVI-estimators. Under convenient but soft restrictions on the underlying mo del, these estimators are consis- tent and asymptotically normal. The behaviour of the PORT-MO p VaR-estimators is studied for finite samples through Monte-Carlo simulation experiments.
关键词：asymptotic behaviour; heavy tails; high quantiles; mean-of-order-p estimation; Monte- ; Carlo simulation; PORT methodology; semi-parametric methods; statistics of ex- ; tremes; value-at-risk