Expected move calculator
Volatility and days in, a range and a set of probabilities out. The three numbers people quote as the chance of finishing in the money are three different numbers, and this prints all three with the gaps between them.
Worked example — At 55% volatility over 30 days, the one standard deviation range is: $85 to $117. From a $100 underlying: up $17.08, down $14.59, not the symmetric ±$15.77 most calculators print.
Your own drift assumption 3
The symmetric formula would say plus or minus $15.77 either way, which is not the same range.
Lognormal prices, one constant volatility, continuous trading, and no jumps. Real distributions have fatter tails than this, so treat the band as the model's answer rather than as a forecast.
One standard deviation bandRegion tested: above $115
What a win rate is worth once the loss is priced
Expectancy per trade: -$50.00. Break-even win rate at this payoff: 80.0%. Over 100 trades: -$5,000.
The loss is 4.00 times the credit, so the position needs a 80.0% win rate just to break even. A 70% win rate is short by 10.0 percentage points.
The band, against the formula everyone else prints
Every expected-move calculator prints S × σ × √(days/365) and applies it in both directions. That is a symmetric move applied to a variable that cannot go below zero and has no ceiling.
| Method | Lower | Upper |
|---|---|---|
| Lognormal (compounded move) S × e±σ√T | $85.41 | $117.08 |
| Symmetric shortcut S ± Sσ√T | $84.23 | $115.77 |
The symmetric shortcut puts the floor $1.18 below where the model puts it and the ceiling $1.31 below where the model puts it, on these inputs.
Is delta the same as the probability of expiring in the money?
No. Delta is a hedge ratio, e−qT N(d1); the model's own probability of finishing past a level is N(d2). On the default inputs, delta reads 21.6% while the model's own probability is 17.2%, a gap of 4.3%. Both are risk-neutral quantities regardless: they assume the underlying drifts at the risk-free rate less the dividend yield, not at what you actually believe. The real-world probability, at an assumed 8% annual drift, is 17.8%.
What's the difference between touching and finishing?
Finishing is where the price ends up at expiry. Touching is whether it ever trades through the level before then, which comes from the first-passage law for Brownian motion rather than from doubling the finishing probability by convention. On the default inputs, the chance of touching $115 before expiry is 35.6%, against a 17.2% chance of finishing above it, a gap of 18.4% percentage points. A short position comfortable at expiry can still be closed out at a loss on the way there, and touch is the number that says how likely that is.
A 70% win rate sounds like an edge and usually is not: at four to one against, break-even is 80%, which is what the short-premium block inside the calculator is for. Every number here assumes lognormal prices, one constant volatility, continuous trading, and no jumps; real distributions have fatter tails, so the band understates how often the extremes happen, and gap risk is not in the touch number at all. To measure volatility from a quoted price, use the implied volatility calculator; to price the option itself, the Black-Scholes calculator; to size whatever you conclude, the position size calculator.
The next question after this one
Implied volatility calculatorCalculatorThe volatility input this page needs, solved from a real option price instead of assumed.Open nextOther questions
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What Pro adds here
Fat-tailed and jump-diffusion variants of the same band, plus the expected move implied by a straddle price rather than by a volatility input, are Pro features. The launch list sends one email at launch.