This calculator computes the model probability that a stock finishes above or below a chosen price level by expiration, using the log-normal distribution with implied volatility and zero drift. Entering a spread's breakeven as the level approximates the structure's probability of profit; entering the short strike approximates the probability the strike holds.
Log-normal model with zero drift, the same family of assumptions behind common POP displays. Real return distributions have fatter tails than the model.
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The stock's price at expiration is modeled as log-normal: log returns are normally distributed with a standard deviation of implied volatility scaled by the square root of time, and the drift is set to zero. The probability of finishing above a level K from price S is then N( (ln(S/K) - 0.5 x sigma^2 x T) / (sigma x sqrt(T)) ), where N is the standard normal distribution function. This is the same family of arithmetic that produces the POP figures on options platforms, which is exactly why its assumptions are worth knowing.
A $100 stock, a $95 level, implied volatility 30, 30 days: T is 0.0822, sigma is 0.30. d = (ln(100/95) - 0.5 x 0.09 x 0.0822) / (0.30 x 0.2867) = (0.0513 - 0.0037) / 0.0860 = 0.553, and N(0.553) is about 0.71. The model says roughly a 71 percent chance of finishing above $95, and 29 percent below.
Implementations differ in the drift assumption (zero, the risk-free rate, or a carry-adjusted rate), in whether they test the breakeven or the short strike, and in which volatility input they read. None of the variants is wrong; they answer slightly different questions. The number to trust is the one whose assumptions are stated, and any of them describes model probability, not edge: the POP article explains why a high probability and a fair price can coexist.
The model-implied chance that the position finishes expiration with any profit, computed from the break-even price, the current price, the implied volatility and the time left. It describes the distribution the options market is pricing, not a forecast of where the stock will go.
It is the probability at expiration under the pricing model's assumptions. Real positions are often closed early, volatility changes after entry, and the model's distribution is not the market's; a trade journal is the only place an actual win rate comes from.
A larger credit moves the break-even further from the current price, which raises the probability of finishing profitable, and it also raises the loss on the other side. The calculator shows both effects so the trade-off is visible before anything is placed.