How much of the SPX options book is new each day? Open-interest change across 1,081 sessions

Short version of a post on gex.live/research ; the full write-up, definitions and reproduce block live there. Most published dealer-gamma numbers are built from open interest : yesterday's outstanding contracts, multiplied by a convention about who holds which side. Whether the convention is right is a separate question. The prior question is simpler: how much of what trades today was already in that book this morning — and how much of tomorrow's book is being created today? Open interest and volume are enough to answer it, with no assumption about who bought. Sample: SPX and SPXW, 2022-04-14 to 2026-08-14, 1,081 trading days, every expiry within about a month (0DTE plus the 21 nearest), 8.6 million contract-days, 4.3 million with volume. Definitions Per contract (expiry, strike, right) and session D: OI(D) is open interest at the start of D, OI(D+1) at the start of the next session, ΔOI = OI(D+1) − OI(D) , vol the day's volume in that contract. |ΔOI| / vol is a lower bound on how one-sided the day's trading in that contract was — 1.0 means every lot opened (or every lot closed), 0 means opens and closes cancelled. Contracts expiring on D have no next-day OI and drop out of the ΔOI statistics; 4.1% of rows (3.8% of volume) show |ΔOI| > vol, which is impossible (OI snapshot timing) and are excluded. The book grows by 40% of what trades, every day days to expiry on D net ΔOI / volume |ΔOI| / volume (lower bound on one-sidedness) share of volume in contracts whose OI rose contract-days 1–5 37.8% 41.8% 90.3% 813,013 6–21 42.7% 53.3% 81.1% 2,206,446 22+ 42.8% 57.6% 76.5% 831,896 Across the whole book, net ΔOI is 39.9% of the day's volume on the median session (IQR 36.2–44.0%), positive in every year and every expiry bucket: the SPX book is always being built faster than it is unwound, until expiry does the unwinding. Far expiries are open-and-hold (a day's trading in a 22+ DTE contract is at least 58% one-sided); the nearest expiries churn (42% at 1–5 DTE). Per contract-