Markets close. Risk doesn't. This is the live cost of the dark hours — the gap coefficient Perpify's engine applies while the S&P 500 sleeps.
When the market sleeps, price lives in a corridor priced by this model — and pushing on the walls costs margin and funding every hour. While the S&P is dark the engine confines its mark to anchor × (1 ± κσ); sustained pressure at the edge re-anchors the corridor, but each step raises margin +25% and lifts the funding clamp +50%. Real news walks out. Manipulation pays rent.
P(|gap| > x), by dark-period class — weekends carry the fatter tail
Share of sessions per 0.2% bin, normalized within each class
Largest |gap| each year, 1995–2026 — tail risk clusters in regimes, it doesn't average out
Half arrived after a weekend or holiday close
| # | Reopen date | Gap | Dark period | Context |
|---|
Gap = today's official open ÷ previous session's official close − 1: the move that happens entirely while the market is closed and no position can be adjusted. A reopen is classed weekend/holiday when the previous session is ≥3 calendar days back. Dataset: SPY daily OHLC, unadjusted, 1995-01-04 → 2026-07-17 — 7,936 reopens (6,291 weeknight, 1,645 weekend/holiday). SPY's four ex-dividend days per year each add roughly 0.3–0.4% of mechanical down-bias, below the 0.5% stat threshold.
The gap coefficient shown above is the v0 margin scalar Perpify applies during dark periods: weeknight baseline 1.00σ (σ = 0.65%), weekend/holiday 1.25σ (σ = 0.81%, a 1.55× variance premium) — the σ-basis anchor of a calibration range of 1.2–1.5 that will be conditioned up by realized-vol regime and scheduled events. Weekend fat tails come from event clustering, not duration alone: 65.5 dark hours hold 3.7× the weeknight's dark time but only 1.55× its gap variance — until the years where they hold everything.
The price band (live at the top of this page while the S&P is dark) is the corridor the engine confines its mark to when there is no spot anchor: anchor × (1 ± κσ), with σ from this model per dark-type × regime and κ = 4.0 — the P99.5 of |gap| ÷ RMS across all 7,936 normalized reopens. Calibrated, not chosen: legitimate moves push the corridor's walls out roughly once a year, while a manipulated print pays +25% margin and +50% funding-clamp escalation per step. Single-stock markets carry a fatter κ (NVDA 4.55) for their earnings-jump share. Reproduce it: python3 risk/gap/calibrate_kappa.py.
Earlier Perpify materials claimed "38% of trading days open with a gap larger than 0.5%." When we calibrated the model against the full 31-year series, the measured number was 28.5%. We corrected every document. A venue whose product is published, replayable methodology cannot carry an unverifiable stat — including its own.
Reproduce every number on this page: python3 risk/gap/gap_stats.py against risk/data/spy_daily.csv. The dataset refreshes with each Weekly Gap Report.