Expected Move & Probability Calculator
The price range an option’s implied volatility points to, and its odds.
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- Free preview: the 1-standard-deviation expected move in full, with the first rows of each table (up to 3) and a watermarked chart; every other figure is hidden.
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Chance of ending in each band of prices
Lognormal price by the date, in 24 equal bands across ±3σ.
Ranges and probabilities
How this was calculated
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For education only, not investment advice: no tool here tells you what to buy, sell or hold. Results use only the figures you enter, the files you load (read in your browser, never uploaded) and the published rules each page names. Check them against your broker's or exchange's own figures, and consider a licensed or registered adviser for advice on your situation.
About the Expected Move & Probability Calculator
An option’s implied volatility says how much the market prices in for the underlying to move. This calculator turns it into the expected move: the 1σ (one standard deviation) move by a date you choose, the 1σ and 2σ price ranges — straight (price ± the move) and lognormal (price × e^±σ√T) — the chance of ending inside a range or above or below a level under a lognormal price, the rough chance of touching a level on the way, and the usual daily move.
You can start from the implied volatility, or from the price of an at-the-money straddle (call plus put), which gives the move directly. Count days as calendar days (365 a year) or trading days (252 a year). Paste your own past IV readings to see the IV rank and IV percentile of today’s figure.
It works for shares, indices, futures and currencies in any market, with the figures you type: no market data is used, and the ranges describe what the volatility you entered implies, not where the price will go.
How to use it
- Enter the price now, then the implied volatility as a percentage a year — or switch to the straddle and enter the at-the-money call plus put.
- Enter the days to the date you care about, and whether they are calendar days or trading days.
- Optionally add a range or a level to get the chance of ending inside it, above or below it, and of touching it.
- Optionally paste your own IV readings (one per line, or separated by commas) for IV rank and IV percentile.
- Read the 1σ move, the ranges and the probabilities, then copy the summary or download the table as CSV — with a pass, or after unlocking this result.
Examples
σ√T = 0.30 × √(30 ÷ 365) = 0.086007
1σ move ±8.60 · 91.40 to 108.60 (normal), 91.76 to 108.98 (lognormal) · 2σ 82.80 to 117.20 · P(91.40 < price < 108.60) 68.39% · P(above 108.60) 15.81%
Price 100, at-the-money straddle 4.5743
1σ move ≈ 4.5743 ÷ 0.797885 = ±5.733 (the exact move at 20% volatility and 30 days is 5.7338)
Your readings 20, 25, 30, 35, 40 (%); IV now 30%
IV rank 50% (30 is half-way from 20 to 40) · IV percentile 40% (2 of 5 readings are below 30)
Common uses
- See the 1σ and 2σ ranges a 25% implied volatility gives a share over the next 30 days.
- Turn a straddle price into the move it prices in before an event.
- Check the chance, under the model, that a price ends inside your range or above a level by a date.
- Compare today’s implied volatility with your own past readings.
The formulas
- The move as a share of the price: σ_T = σ × √(days ÷ basis), with a basis of 365 calendar days or 252 trading days a year.
- 1σ move = S × σ_T; the normal range is S ± S σ_T and the lognormal range S × e^(±σ_T); 2σ doubles σ_T.
- Chance of ending above K = N(d₂), d₂ = [ln(S/K) + (μ − σ²/2)T] ÷ σ√T: the lognormal property of prices in the Black–Scholes model (Hull, Options, Futures, and Other Derivatives, ch. 15), with a drift μ of 0 or r − q.
- Touching a level ≈ 2 × the chance of ending beyond it: the reflection principle, exact for a random walk with no drift and an approximation here.
- From a straddle: an at-the-money straddle is worth about √(2/π) ≈ 0.7979 of the 1σ move, so the move ≈ straddle ÷ 0.7979 (Brenner and Subrahmanyam).
- IV rank = (IV now − lowest reading) ÷ (highest − lowest); IV percentile = the share of your readings below IV now.
Reading the results
- One standard deviation covers about 68% of outcomes and two about 95% under the model; the lognormal range is a little higher than the straight one because prices cannot fall below zero.
- The probabilities follow from the volatility you entered and the lognormal model. They are hypothetical, change with your inputs, and say nothing about where a price will actually go.
- IV rank and percentile compare today’s volatility with the readings you pasted: a rank of 50% means half-way between your lowest and highest reading.
What it leaves out
Jumps and gaps (an earnings report, a central bank decision), which the lognormal model understates; volatility that changes over time or differs across strikes (the smile); the bid–ask spread of the options the volatility comes from; and fat tails, which make big moves more common than the model says. Each can make the real range wider than the one shown.
Limitations
- A lognormal price with constant volatility: real prices jump and their volatility changes.
- The chance of touching a level is an approximation (twice the chance of ending beyond it).
- The straddle shortcut is accurate near the money and for short periods.
- It calculates from your numbers and uses no market data: it says nothing about where any price is going.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
What do I get without a pass?
Without a pass, Expected Move & Probability Calculator shows the 1-standard-deviation expected move in full, with the first rows of each table (up to 3) and a watermarked chart; every other figure is hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
What is the expected move of an option?
The one-standard-deviation move the implied volatility points to by a date: the price × the volatility × √(time in years). For a price of 100, 30% volatility and 30 days it is about ±8.60, a range of 91.40 to 108.60.
Why are there two 1σ ranges?
The straight range adds and subtracts the move; the lognormal range multiplies the price by e^±σ√T, the shape prices have in the Black–Scholes model. The lognormal one sits a little higher because a price can rise without limit but cannot fall below zero.
How do I get the expected move from a straddle?
Divide the at-the-money straddle price (call plus put) by about 0.7979. A straddle of 4.57 on a price of 100 implies a 1σ move of about 5.73.
What is the difference between IV rank and IV percentile?
IV rank says where today’s volatility sits between the lowest and highest of your readings; IV percentile says what share of your readings were below it. With readings of 20, 25, 30, 35 and 40% and 30% today, the rank is 50% and the percentile 40%.
Should I count calendar days or trading days?
Match how the volatility was quoted. Option implied volatilities are usually annualised over calendar days (365); some traders use trading days (252) for daily moves. The tool does either.