Modeling dynamic VaR and CVaR of cryptocurrency returns with alpha-stable innovations

We employ alpha-stable distribution to dynamically compute risk exposure measures for the five most traded cryptocurrencies. Returns are jointly modeled with an ARMA-GARCH approach for their conditional mean and variance processes with alpha-stable innovations. We use the MLE method to estimate the parameters of this distribution, along with those of conditional mean and variance. Our results show that the dynamic approach is superior to the static method. We also find out that these risk measures of five cryptocurrencies do not offer the same pattern of behavior across subperiods (i.e., pre-, during- and post-COVID pandemic).