Options research

Is the probability of touch really twice the probability of finishing in the money?

By Nikolai Alexander · 2 November 2026 · stocks 2016–2026, S&P 500 since 1990

Option sellers learn a rule of thumb: a strike is touched about twice as often as it finishes in the money. I tested it on 469 S&P 500 stocks over ten years, on the S&P 500 index since 1990 and on 18,462 earnings reports. On average the rule holds remarkably well. Only two things break it: earnings gaps, and the trend.

Where the rule comes from

Picture a stock price as a random walk without a trend, and a strike above the current price. Every path that reaches the strike is, from that moment on, equally likely to end above it as below it. So of all the paths that touch the strike, half finish beyond it: the probability of touching is twice the probability of finishing beyond. Mathematicians call this the reflection principle.

The rule has a useful property: it does not depend on how volatile the stock is. A wrong volatility estimate changes how often a strike is touched, but not the ratio. Only two things can break it. Jumps can carry the price past the strike and leave it there, so that a "touch" is already a finish. And a trend tilts the paths after the touch toward one side.

How the strikes were counted

• 469 S&P 500 stocks, 2016 to 2026, and the S&P 500 index since 1990, daily prices. A new set of strikes starts on every trading day.
• Strikes at 0.5, 1, 1.5 and 2 standard deviations above and below the starting price, scaled with the stock's realized volatility of the previous 20 trading days and the length of the term.
• Terms of one week, one month and three months (5, 21 and 63 trading days).
• Touched: the day's high (calls) or low (puts) reached the strike during the term. Finished beyond: the close on the last day of the term was past the strike. The ratio is touched divided by finished.
• Earnings: 18,462 reports with their time of day. The reaction day is the same day for reports before the open, the next day for reports after the close.

On average, the rule holds

Across all 469 stocks, a strike one standard deviation away was touched in 33.0% of one-month terms and finished beyond in 16.8%: a ratio of 1.96. Over three months it was 2.02. On the S&P 500 since 1990 it was 1.99 for one month and 2.00 for three months; only one week was lower, at 1.88. The random-walk textbook says 31.7% and 15.9%. For a rule that rests on a simple model of prices, that is close. The gray dots are the average of calls and puts together. The trend is in them too, but it pushes the two sides in opposite directions, so it largely cancels out: puts (red) sit above 2 and calls (green) below, the more so the longer the term and on the index. The second break below shows what the average hides. Within a single trading day, SPY showed a similar pattern: a level 1% away from the open was touched on 29.1% of days and closed beyond on 16.0% (0DTE odds on SPY).

Break 1: earnings gaps

The first break does not depend on the direction of the market, and it hits calls and puts alike. When a stock reported earnings before the options expired, the ratio fell below 2: from 2.01 to 1.78 for options with one week to expiry, and from 2.01 to 1.90 with one month. Options with three months to expiry almost always span a report, and there the ratio stayed at 2.

In probabilities: without a report, a touched strike finished in the money about half the time (50%). With a report before expiry, it was 56% for one-week options and 53% for one-month options. For one-week options the effect showed up in every single year from 2016 to 2026 and at every strike distance. To make sure the reports cause it and not chance, I ran the same test with fake report dates, ten days before or after the real ones: the effect disappeared, so it belongs to the reports themselves.

But the report alone does not decide it. What matters is the day the strike was touched. The chart takes only options with a report before expiry and compares strikes touched on the earnings reaction day with strikes touched on another day of the same term.

The timing of the touches explains it. A strike touched on the reaction day finished in the money about six times in ten, at every expiry (average 58 to 61%; one week: puts 58%, calls 63%). The gap had already carried the price past the strike, and the close of that day decided most of the outcome. After the gap, the price behaved like an ordinary random walk again: no rebound that would pull it back, and no follow-through that would push it further. A strike touched on another day finished in the money about half the time, just like in terms without a report.

Break 2: the trend

The second break splits the two sides. On average they cancel out, but separately they do not. A rising market tilts every path after a touch upward: touched call strikes finish in the money more often than half the time, touched put strikes less often. Across the 469 stocks, the three-month ratio was 2.36 for puts and 1.80 for calls, and the gap grew with the stock's own trend. On the S&P 500 since 1990 it was wider still: 2.98 for puts, 1.60 for calls.

To see the trend at work, the long bear markets are the test case. They can only be measured on the index: the stock prices here start in 2016 and contain no long bear market, and going further back with today's index members would hide exactly the companies that collapsed in those bear markets (survivorship bias), which would make the effect look smaller than it was. The S&P 500 itself has no such gap and goes back to 1990.

The two long bear markets turned it around. From March 2000 to October 2002 and from October 2007 to March 2009, a three-month put strike was touched more than half the time, and 59% of the touched put strikes finished in the money. In all other years, only 27% did. Those other years were mostly rising markets, but they also include sharp falls such as the 2020 crash and the 2022 decline.

Touched: share of three-month terms in which the strike was touched. Then finished: of those touched strikes, the share that finished in the money.

So the same touch meant very different things: in a bull market, a touched put strike usually came back; in a bear market, it usually stayed in the money.

What it means for option sellers

For most strikes, most of the time, "a touched strike finishes in the money about half the time" is a good working assumption, and with it, "the probability of touch is about twice the probability of expiring in the money". Where it needs care:

• With earnings, watch when the strike is touched. A strike touched on the earnings reaction day finished in the money about six times in ten (one week: 58% for puts, 63% for calls), not half the time. A strike touched on another day of the same term behaved like an ordinary touch.
• No rebound after the gap. After the earnings gap, the price moved like an ordinary random walk again. There was no rebound that pulled it back to the strike, so a strike the gap jumped past stayed in the money more often than not.
• Halving the probability of touch is too optimistic across a report. For one-week options with a report before expiry, the ratio was 1.78 instead of 2: the chance of finishing in the money was about 12% higher than the rule of thumb says.
• A touch on the reaction day matters for defensive rolls. If a short strike is touched on the reaction day, it is more likely than not to expire in the money: about six times in ten, at every expiry. Waiting for the price to come back is a weaker bet than after an ordinary touch, which comes back about half the time.
• The trend decides which side comes back. In mostly rising years on the S&P 500, only 27% of touched three-month put strikes finished in the money, while 63% of touched call strikes did. In the long bear markets it flipped: 59% of touched put strikes stayed in the money. The "half" of the rule is the average of two sides that behave differently.

The probability of finishing in the money is also not the same as delta, the number it is often confused with: is delta the probability of expiring in the money?

Data and notes

• Daily prices from Yahoo Finance: 469 current S&P 500 members, 2016–2026, split-adjusted but not dividend-adjusted, as options settle on the price; the S&P 500 index (^GSPC) from 1990. Earnings dates and times from Yahoo Finance; where the time was missing, the reaction day is the day with the larger opening gap.
• Strikes are scaled with realized volatility (20 trading days, close to close). The rule is usually quoted with implied volatility; the ratio does not depend on the volatility used, the touch rates do. For the earnings test, the volatility excludes the earnings reaction days.
• Survivorship: the stocks are today's S&P 500 members, so companies that dropped out of the index are missing.
• Terms start on every trading day and overlap; a check with non-overlapping starts gave the same picture. Daily bars count a gap through the strike as a touch.
• The bear markets are dated from the S&P 500's peak to its trough (24 March 2000 to 9 October 2002, 9 October 2007 to 9 March 2009).
• All numbers count what happened in the past. They are not probabilities for the future, not forecasts and not financial advice.