  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.
