Probability of touch calculator
Ending past your strike and touching it on the way are two different odds. How often will the stock dip to your strike first and make your stomach drop? Type in the strike and the IV and see both, side by side.
How it works: the page treats the stock as a random walk sized by its implied volatility, with no drift up or down. Finishing past the strike uses the same normal curve as Black-Scholes: it asks how many standard deviations away the strike is by expiry. Touching uses the reflection rule: every path that ends past the strike touched it, and for each of those there is a mirror path that touched it and came back. So touching comes out close to twice the finish chance. The page works out the exact model figure, then shows the quick 2× figure next to it.
Why touching is about twice as likely
Picture the stock hitting your strike halfway through the month. From there it's close to a coin flip whether it ends above or below. So for every path that touches and stays past the strike, there is roughly one that touches and comes back. That is where "about 2×" comes from. For a seller this matters: a put you sold can go in the money for a few scary days and still expire worthless. Knowing the touch chance tells you how often to expect those days. See probability of assignment explained.
Where the model falls short
Real stocks don't move like a smooth random walk. They gap on earnings and news, they trend for months, and their IV changes every day. A gap jumps past your strike with no "touch" in between. So treat these numbers as the odds the market is pricing today, not a forecast. In the wheel strategy, the useful question is not "will it touch?" but "if it touches, am I fine owning the stock at this strike?"
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