The short answer
They are different questions and they get different numbers.
- Probability of expiring in the money asks about the destination. Will the index settle above 8,090 on this expiration date?
- Probability of touch asks about the path. Will the index trade at 8,090 at any point before that date, whether or not it is still there at the end?
The second is always at least as large as the first, because every path that finishes beyond a level had to cross it. For a level comfortably away from the money, the second is close to twice the first.
That factor is not a rule of thumb somebody made up. It follows from the reflection principle, and knowing where it comes from is also how you know where it stops working.
Why the answer is about double
Take a level above the current forward and a random walk with no drift. Every path can be sorted into three kinds: paths that never reach the level, paths that reach it and finish above, and paths that reach it and finish back below.
The reflection principle says the third group is the same size as the second. For every path that touches the level and comes back, there is a mirror image of it, reflected at the moment of first touch, that touches and continues on to finish above. The two groups are in one-to-one correspondence.
So the paths that touch are the paths that finish above, counted twice. If the market prices a 6 percent chance of settling above a level, it is implicitly pricing something near a 12 percent chance of trading there first.
The same thing with live numbers
Here is one chain, dated. On 2026-09-22, the SPX option chain expiring 2026-10-16, twenty-four days out, was quoting a forward of 7,780.60 with an at-the-money implied volatility of about 11.0 percent, read from the delayed Cboe chain that afternoon.
The settlement probabilities it priced:
- Settling above 8,090 (about 4 percent above the forward): 6.0 percent.
- Settling below 7,470 (about 4 percent below): 8.0 percent.
- Settling inside the central 68 percent band, 7,591 to 7,992: 68 percent by construction, which means 16 percent beyond each edge.
Those are read off the risk-neutral density recovered from the whole chain, not computed from the at-the-money volatility alone, and the two give different answers. A lognormal at 11.0 percent over the same twenty-four days puts its one standard deviation band about 440 points wide, where the published band is 401, and prices settling above 8,090 at about 8 percent rather than 6. The recovered density is narrower in the body than that lognormal and thinner on the upside, which is the skew the last item in the next section is about.
Apply the doubling and the picture changes character. The upside level the chain prices at a 6 percent chance of holding is near a 12 percent chance of being printed at least once. The band that contains the settlement two times in three has edges that are each near a one in three chance of being touched, so the band is a statement about where price ends up, not a corridor it stays inside.
Options implied probability covers how those settlement numbers are extracted from the chain, and the live ladder publishes them for SPX, SPY and QQQ. Neither publishes a touch probability, which is why the arithmetic above is the reader's own to run.
Where the doubling breaks
Four conditions, and each one is visible before you use the number.
Drift. The reflection argument needs a driftless walk. Under the risk-neutral measure the reference point is the forward, not spot, and those are not the same number. On the chain above, the forward sat about 19 points above spot. Measuring a level's distance from spot and then applying a rule that assumes no drift double-counts the difference.
Levels near the money. Doubling a 45 percent settlement probability gives 90 percent, and doubling anything above 50 percent gives an impossible answer. The approximation is for levels far enough away that the finishing probability is comfortably below half. Near the money the true touch probability approaches one and the rule stops being informative well before it stops being arithmetic.
Continuous monitoring. The principle counts every instant. A level touched for one print in a thin session counts as a touch, and a level breached only in overnight futures while the cash index was closed may not count at all, depending on which series you are watching. The definition of touched has to be fixed before the number means anything.
Skew. The chain does not price up and down symmetrically. On the reading above, 4 percent below the forward carried a higher settlement probability than 4 percent above it, which is the usual shape for an index. The doubling applies to each side separately, using that side's own settlement probability, rather than to a symmetric band.
Which question your position is actually asking
This is where the distinction earns its keep, because different instruments care about different halves.
A European, cash-settled index option such as an SPX contract pays on the settlement value alone. A path that traded through the strike and came back pays nothing. Only the destination matters.
An American-style option on a single stock can be assigned before expiration, and the holder's incentive to exercise early rises as the contract goes deep in the money or as a dividend approaches. That is much closer to a path question than a destination question.
A stop order is entirely a path question. So is a margin call, an alert, and any level-based rule that fires on a print rather than on a close. Pricing those against a settlement probability understates how often they trigger, by roughly the factor of two above.
Pin risk at expiration covers the case where price sits on the strike at the end, which is the uncomfortable overlap of the two questions.
The limit that applies to both
Every probability above is risk-neutral. It is the price of a payout, not a frequency count, and option prices carry a risk premium that sits heaviest on downside protection. The priced odds of a large decline run above the rate at which declines of that size have happened. Doubling a risk-neutral settlement probability produces a risk-neutral touch probability, with the same premium still inside it.
Educational content, not financial advice. See our risk disclosure.