# Options implied probability, from the delayed Cboe chain Source: SquawkFlow URL: https://squawkflow.com/odds Type: Risk-neutral probability extracted from listed option prices Symbol: SPX Expiration: 2026-09-28 Captured: 2026-09-25 16:14 ET > A risk-neutral probability is what the option market charges for a payout, not a count of how often the outcome has happened and not a claim about how often it will. Read off the delayed Cboe chain, mid-market, with no discounting applied. --- ## SPX implied distribution for 2026-09-28 - Days to expiration: 0 - Forward measured from put-call parity: 7713.35 - At-the-money implied volatility: 16.70 percent - Implied median settlement: 7715.78 - Implied quartiles: 7686.06 to 7743.78 - Central 68 percent of the implied distribution: 7670.59 to 7757.13 - Expected absolute move from the forward: 0.47 percent Quantiles and the central 68 percent band are read off the risk-neutral density recovered from this chain. Expected absolute move is the risk-neutral expectation of the distance from the forward at settlement, which is not the same thing as a one standard deviation band. ## Priced odds by level | Level | From forward | Priced above | Priced below | Cross-check | | --- | --- | --- | --- | --- | | 7560 | -1.99% | 99.5% | 0.5% | 99.5% | | 7635 | -1.02% | 94.5% | 5.5% | 94.9% | | 7715 | +0.02% | 50.8% | 49.2% | 50.7% | | 7790 | +0.99% | 4.5% | 95.5% | 4.2% | A level is left out when its two methods disagree by more than 5 points or by more than 25 percent of the smaller side's probability, when the cross-check cannot see enough of that tail to check it, or when the quotes there do not express a probability. Every level left out is listed below the table with its reason. ## Levels left out - 7450: left out because the quotes either side do not express a probability: resting at the minimum tick, or steeper than their own strikes. - 7480: left out because the quotes either side do not express a probability: resting at the minimum tick, or steeper than their own strikes. - 7865: left out because the independent cross-check disagreed beyond the publication rule. - 7895: left out because it sits at the edge of what the independent cross-check can recover, so nothing corroborates it. ## Method - Method: digital_spread_adjacent_strikes - Arithmetic: P(S_E > K) = -dc/dK, where c is the undiscounted call curve and dc/dK is interpolated to K between the first differences of the adjacent listed strikes either side of it - Cross-check: breeden_litzenberger_smile, an independent implementation run on every published level - Forward: put_call_parity_median, dispersion 0.000004 - Discounting: not applied, bound on the omitted term 0.006 percent - Strikes: 243 quoted, 100 used, 3 dropped by the call-curve shape check, 100 blended from the call and put markets, largest gap 0.70 - Cross-check density: 0.0000 of negative density floored - Option root: SPXW, settles at the close - Methodology version: implied-odds-1.1.0 ## Publication rule A reading is published only when the expiration settles within 90 days, at least 8 strikes carry a usable quote on both the call and the put side and agree about the forward to within 0.6 percent, at least 12 strikes with a two-sided quote worth 0.05 or more survive the call-curve shape check inside the fitting window, the level sits strictly inside the quoted strike range, the two strikes bracketing it are within 1.5 percent of the forward of each other, the recovered distribution integrates to between 0.95 and 1.05 with no more than 0.01 of negative density floored away, and the two independent methods agree within 0.05 in probability and within 25 percent of the smaller side's probability, the tail, whichever is tighter. The relative test forgives only the tail mass beyond the last quoted strike that the distribution could not see, only in the direction that missing mass can explain, and a level where that mass is more than 25 percent of the tail is not checked at all and is withheld. Anything else is served as absence with the reason named. ## Known biases - Risk-neutral is not real-world. Option prices embed a variance and jump risk premium, so downside probabilities read higher than realised downside frequency and upside probabilities read lower. - SPY and QQQ options are American style. An early-exercise premium sits in those quotes and widens the extracted distribution slightly. SPX is European and carries no such premium. - Strikes are discrete. The derivative is read from first differences between adjacent listed strikes, interpolated to the level, so the answer is a local average over the strikes it leaned on, published as bracketLow, bracketHigh and bracketWidthPct. - Quotes are delayed and mid-market. A midpoint is not a traded price, and a wide spread on a quiet strike moves the reading. - No discounting is applied. Probabilities are stated under the forward measure, which leaves a relative error of order rT, bounded and published as discountingOmittedBoundPct. - The forward is measured from put-call parity on this chain rather than assumed from an interest rate curve, so a chain whose strikes disagree about their own forward is served as absence instead of a number. - Around the forward the call curve is a weighted blend of the quoted call mid and the put mid carried across by put-call parity, weighted by distance from the forward and by how tightly each is quoted, not either quote on its own, so the value there is a price nobody quoted. It is used because a hard switch from one side to the other at the forward leaves a kink the difference misreads. The number of strikes it touched is published as strikesBlendedFromBothSides, and the largest gap between the two markets at any of them, in price, as blendLargestGap. - A strike whose value on that curve breaks the falling, above-intrinsic shape a call curve must have leaves the calculation rather than being smoothed back into it, so a reading can rest on fewer strikes than the chain lists. The count is published as strikesDroppedForArbitrage. - The cross-check density is the second derivative of a fitted smile, and a fit can dip below zero in the wings. The negative part is floored at zero and the rest renormalised, which is a repair of the fit, not of any quote. The mass it removed is published as densityNegativeMass, and past maxDensityNegativeMass the reading is served as absence instead. Other risk-neutral readings off the same chain. Not comparable to a historical frequency, a backtest or any real-world probability. Nothing here is advice or a recommendation. ## Citation Source: SquawkFlow, https://squawkflow.com/odds Retrieved: 2026-09-28 04:48 ET Attribution: cite the page URL rather than a copied number. Levels are recomputed every session, so a number without its date is wrong within a day. SquawkFlow publishes market-structure data and education. Nothing here is investment advice, a price target or a recommendation, and we have no order execution.