This paper investigates some properties of derivative measures of the Value at Risk (VaR) of random variables modeling the stochastic behavior of a portfolio asset. Specifically, coherentness and convex properties of the conditional, the tail VaR and the standard deviation are established. Moreover, a new version of high risk scenario is characterized and bivariate densities are modeled via copula approach.

risk management, Value at Risk, copulas, extreme values distribution, Pareto distributions