Our [OCC's] research found that [Levy] distributions provided estimates of future distributions that were much more consistent (stable) over time than those that either ignored higher moments than variance or relied solely on past extreme instances that had occurred during a past data sampling window. While on average the typical stock alpha was about 1.65, there was a wide distribution about that average (1.3 to virtually 2.0). So OCC uses stock specific values for all four parameters of a stable [Levy] distribution (including non-symmetry) and assesses the critical tail values (I% and 99% cutoffs) individually. This led to different likely movements across stocks and larger down moves than up moves as well.

Donald MacKenzie, An Engine, Not a Camera, loc. 937