Levy distributions yield more stable estimates of extreme moves than variance-based methods

Evidence

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, 937

Categorization

• XREF: connects to: Under a Gaussian distribution extreme tail events become effectively impossible — Mark Blyth, Austerity: The History of a Dangerous…, 106; A single exponent alpha parametrizes a family spanning normal to wildly fatal-tailed distributions — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 479; Levy distributions keep identical form across every timescale, making scale irrelevant — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 492 (+5 more)

Broader Connections

• Deliberately assuming wild randomness can paradoxically keep markets mild #exemplifies (0.80) — Donald MacKenzie, An Engine, Not a Camera, 1169