Black-Scholes with VIX1D under-prices ATM 0DTE entry premium by roughly 85%

Across thousands of validated trades, real entry mid / BSM entry premium has a median of 1.85. The error is stable, asymmetric between entry and exit, and large enough to manufacture phantom edge on a signal that has none.

The measurement

Take the strictly-validated trades from a four-year SPX 0DTE backtest, price each ATM entry with Black-Scholes using VIX1D as sigma, and compare against the real Databento OPRA mid at the same timestamp:

Entry leg: real mid / BSM premium — median 1.853, mean 1.883, interquartile range 1.62–2.10
Exit leg: median ratio 1.25

The entry-side error is stable (cross-sectional std ≈ 0.45) and in one direction: BSM computes roughly half the premium you would actually pay. Equivalently, VIX1D understates the IV that market makers actually quote for same-day ATM optionality by ~46%.

Why the gap exists

VIX1D is a next-day variance index. At a 9:40–11:00 ET entry, the relevant vol is the remaining 4–6 hours of today, quoted by dealers who carry the gamma risk of an expiring contract. That gamma risk premium is baked into real 0DTE bid/ask and simply absent from a previous-close variance measure. By the exit leg, T→0 has collapsed the sigma-sensitivity, which is why exit pricing is far less wrong (1.25) than entry pricing (1.85).

The asymmetry is the operationally important part: no single sigma multiplier can fix both legs. Per-exit-reason ratios diverge further — EOD exits ran ~0.49 (BSM overstates real PnL) while reversal exits ran ~2.48 (BSM understates real losses, because fast adverse moves coincide with spread blow-outs and IV crush).

What it does to a backtest

Understating entry premium understates the cost basis of every trade. On this strategy the BSM ledger showed +1,217 points for the best policy over the Databento window; direct measurement of the same trades showed −3,357 points (−$107K/year). The signal itself was near-null at the SPX level — the entire apparent edge was pricing error plus a selection filter (see the selection-bias note).

Practice

Treat BSM-with-VIX1D 0DTE PnL as a relative screen, never as evidence a strategy is profitable.
If you must calibrate proxy to real, calibrate per leg and per exit reason — and expect the ratios to drift year to year (they did: EOD ratios decayed monotonically from 0.53 to 0.45 over three years).
The only defensible go/no-go input is real quotes: buy at ask, sell at bid, every trade.

Full numbers are in the negative-result paper on the research page.