Do coherent risk measures identify assets risk profiles similarly? Evidence from international futures markets

Abstract

The authors consider Lévy processes with conditional distributions belonging to a generalized hyperbolic family and compare and contrast full density-based Lévy-expected shortfall (ES) risk measures and Lévy-spectral risk measures (SRM) with those of a traditional tail-based unconditional extreme value (EV) approach. Using the futures data of leading markets the authors find that ES and SRM often differ in recognizing the risk profiles of different assets. While EV (extreme value) is often found to be more consistent than Lévy models, Lévy measures often perform better than EV measures when compared with empirical values. This becomes increasingly apparent as investors become more risk averse.

Keywords

• expected shortfall
• extreme value
• generalized hyperbolic distributions
• Lévy-Khintchine formula
• spectral risk measures