Where does SPX actually finish, relative to where it sat at 9:45am? Every trading day, from real 1-minute NBBO option quotes. Filter by overnight and early-session conditions to see whether they move the distribution — and by how much.
Bin width 0.1%. The outline is all days; the filled bars are your current filter, rescaled to the same density so the shapes are comparable at any sample size.
This is the number that decides a butterfly. Read it as: if you pin the body at the 9:45 price, how often does the close finish inside that band?
Excursion is the furthest SPX travelled from the 9:45 price at any point before the close — what a stop or a short wing actually has to survive.
Two different questions, computed on the current filter. Direction is whether the signed move is forecastable; dispersion is whether the width is. R² is the share of variance explained — treat anything under 0.02 as noise.
Ignores the filters above; always the full sample. n is the bucket size — be sceptical of any row under about 60 days.