Spectral measures of risk for international futures markets: A comparison of extreme value and Lévy models

This paper investigates Lévy spectral risk measures (SRM) as a coherent alternative to generalized Pareto spectral risk measures. Specifically, using futures data from major indexes, we consider using SRM for conditional distributions belonging to the generalized hyperbolic family of Lévy processes, and compare and contrast the results with those obtained from the traditional unconditional extreme value approach. Compared with Lévy models, the extreme value model provides poor estimates of quantiles outside the fixed tails, which in turn yield poor estimates of the spectral risk measure itself. The superiority of the Lévy models is increasingly apparent as investors become increasingly risk averse.