Even quite substantial fluctuations in market volatility have limited, slow effects on statistical estimators of the parameters of Levy distributions with infinite variance. In calm periods, estimates of the probabilities of extreme events do not go down much, so margin requirements are not reduced substantially. When extreme events do happen, Levy estimators are also affected only relatively modestly, because Levy distributions with infinite variance "assume" that the probabilities of such events happening are substantial.

Donald MacKenzie, An Engine, Not a Camera, loc. 940