The issue related to the quantification of the tail risk of cryptocurrencies is considered in this paper. The statistical methods used in the study are those concerning recent developments in Extreme Value Theory (EVT) for weakly dependent data. This research proposes an expectile-based approach for assessing the tail risk of dependent data. Expectile is a summary statistic that generalizes the concept of mean, as the quantile generalizes the concept of the median. We present the empirical findings for a dataset of cryptocurrencies. We propose a method for dynamically evaluating the level of the expectiles by estimating the level of the expectiles of the residuals of a heteroscedastic regression, such as a GARCH model. Finally, we introduce the Marginal Expected Shortfall (MES) as a tool for measuring the marginal impact of single assets on systemic shortfalls. In our case of interest, we are focused on the impact of a single cryptocurrency on the systemic risk of the whole cryptocurrency market. In particular, we present an expectile-based MES for dependent data.

翻译：本文探讨加密货币尾部风险量化问题，采用弱相依数据极值理论（EVT）的最新发展作为统计方法，提出一种基于期望分位数的方法来评估相依数据的尾部风险。期望分位数作为概括统计量，如同分位数推广中位数概念般推广了均值的概念。我们展示了加密货币数据集的实证结果，并提出通过估计异方差回归（如GARCH模型）残差序列的期望分位数水平，动态评估期望分位数的方法。最后，引入边际预期短缺（MES）作为度量单个资产对系统性短缺边际影响的工具。本文聚焦于单个加密货币对整体加密货币市场系统性风险的影响，特别针对相依数据提出了基于期望分位数的MES模型。