Expected Move & Probability Calculator
See the price range the option market is implying, and the chance of finishing above or below a level, from the spot price, implied volatility and days to expiry. Uses the same Black-Scholes model as the Greeks calculator. Runs in your browser; nothing is uploaded.
Uses the implied volatility you entered above. Add its 52-week low and high, which many broker option chains and volatility charts show.
A worked example
Say the index is at Rs 24,000, implied volatility is 15%, and there are 30 days to expiry. The expected move for one standard deviation is spot times volatility times the square root of time in years, which comes to about Rs 1,032, or 4.3% of spot, putting the one-standard-deviation range at roughly Rs 22,968 to Rs 25,032. That range is where this calculator puts the odds of finishing at 67.9% if the market's volatility estimate holds, which is the number many traders use to judge whether a strike is close to or far from where the market expects price to land.
Understanding the calculation
- Expected move
- Spot times implied volatility times the square root of (days to expiry divided by 365). Two standard deviations is twice that.
- Probabilities
- The chance of finishing above a level is N(d2) from the Black-Scholes model, with the risk-free rate as the drift. The chance of finishing inside a range is the difference between two of these.
- What the model assumes
- Prices follow a lognormal distribution with constant volatility, so real markets, with fatter tails and volatility that changes, will produce big moves more often than shown.
Common questions
What is the expected move of an option or index?
The expected move is the size of the price change the options market is pricing in over a period, based on implied volatility. The one-standard-deviation move is spot times implied volatility times the square root of time in years. The market is implying roughly a two in three chance that the price finishes within that range.
How is the expected move different from the straddle price?
They are closely related. The at-the-money straddle usually costs roughly 80% of the one-standard-deviation expected move, so traders often read the straddle price as a quick estimate of the move the market expects.
What does the probability of finishing above a level mean?
It is the model-implied chance that the price ends above that level on expiry, using the lognormal assumption behind Black-Scholes. It is a probability of where the price finishes, not of whether it touches the level at some point along the way, which is higher.
Why is the range not exactly symmetrical in probability?
Prices in the model move in percentages, so the distribution is skewed slightly upward. The range shown is spot plus and minus the expected move, and the chance of finishing inside it comes out near 68%, not exactly the textbook figure, for that reason.
Which implied volatility should I enter?
Use the implied volatility of the at-the-money option for the expiry you care about, as shown in your broker's option chain. For an index, India VIX is a 30-day estimate of the same idea for Nifty.
What are IV rank and IV percentile?
IV rank shows where today's implied volatility sits between its lowest and highest level over the past year: 0% means at the low, 100% means at the high. IV percentile is the share of days in the past year when implied volatility was lower than it is now. Traders often read a high rank as options being expensive compared with their own history and a low rank as cheap, but neither is a signal on its own.
Is this a prediction?
No. It shows what the option market is pricing, not what will happen. Implied volatility can be wrong, and real markets have fatter tails than the model, so large moves happen more often than these probabilities suggest.