We investigate Lévy spectral risk measures as coherent alternatives to Generalized Pareto spectral risk measures. In particular this paper conducts an empirical study on conditional distributions belonging to Generalized Hyperbolic family of Lévy processes and compares their risk-management features with traditional unconditional extreme value approach. For frequently used VaR measure, backtesting performance of conditional and unconditional approaches is investigated. The idea is to figure out whether there is any particular model which provides minimum violation of VaR for all indices.