Implied Volatility Calculator
Solve for the volatility that makes Black-Scholes match an option's traded price, with the move it implies.
Implied volatility runs the pricing model backwards. Instead of supplying a volatility to get a price, this implied volatility calculator takes the price the option actually trades at and solves for the implied volatility that would produce it — reading option volatility from price rather than the other way round.
Formula: solves Black-Scholes for the volatility matching the traded price
Your figures
Calendar days. The model converts to years internally.
What the option is actually trading at, per share.
Results
Implied volatility
19.97%
annualised, from the price entered
- Implied move over the option's lifeOne standard deviation, so roughly a 68% chance of staying inside it under the model.
- ± US$5.73
- Intrinsic value
- US$0.00
- Time value in the price
- US$2.49
- Delta at this volatility
- +0.5400
- Vega, per 1% of volatility
- US$0.1138
- Theta, per day
- -US$0.0449
- Solver iterationsBisection, which cannot diverge even where vega is near zero.
- 30
What this means
A price of US$2.49 implies 19.97% annualised volatility. Over the 30 days to expiry that corresponds to a one-standard-deviation move of about US$5.73 either way. Implied volatility is what the price implies under the model's assumptions — it is the market's expectation of movement, not a forecast of direction.
- Each strike and expiry usually implies a different volatility. That pattern is the volatility smile, and it exists precisely because the model's constant-volatility assumption does not hold.
- Implied volatility is normally quoted from the mid price. Using the bid or the ask instead shifts the result.
Implied volatility: 19.97%
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About the Implied Volatility calculation
That figure, labelled IV on most platforms, is how the market's expectation of future movement is read out of a quote. Two options on the same underlying with different implied volatilities are telling you the market expects different amounts of movement over their respective lives.
It is also the number that makes options comparable. A 5.00 premium means nothing on its own — it depends on the strike, the expiry and the share price. The implied volatility strips all of that out and leaves a single figure that can be compared across strikes, expiries and underlyings.
Implied Volatility formula
solve for σ such that:
BlackScholes(S, K, T, σ, r, q) = market price
there is no closed form, so it is found numerically
by bisection between 0.01% and 1000%
implied move over the option's life:
± S × σ × √T (one standard deviation)- σ (sigma)
- The implied volatility being solved for, annualised.
- bisection
- Repeatedly halving an interval known to contain the answer.
- implied move
- One standard deviation of expected movement over the remaining life.
Option price rises monotonically with volatility — higher volatility always means a more valuable option — which is what makes it possible to solve for implied volatility uniquely and what makes bisection reliable. There is exactly one volatility that produces any achievable price.
Bisection is used rather than Newton-Raphson deliberately. Newton converges faster but relies on vega, which approaches zero for deep in- and out-of-the-money options; near-zero vega makes Newton's step enormous and the method diverges precisely where it is most needed. Bisection cannot diverge.
The implied move is the most directly useful output. An implied volatility of 30% over 30 days corresponds to a one-standard-deviation move of S × 0.30 × √(30/365) ≈ 8.6% of the share price — roughly a two-in-three chance of finishing inside that range under the model's assumptions.
Implied Volatility: a worked example
A one-year at-the-money call on a 100 underlying, trading at 10.45, with a 5% risk-free rate.
- Search range0.01% to 1000% volatility
- Price at 20% volatility10.4506
- Difference from market≈ 0
- Implied volatility20.00%
- √T√1 = 1
- Implied move100 × 0.20 × 1 = ± 20.00
20% implied volatility, corresponding to a one-standard-deviation move of ±20 over the year. Reading the price of the same option a week later gives a different figure, and the change is what tells you expectations have shifted.
How to use the Implied Volatility calculator
- Enter the price the option is actually trading at — the mid between bid and ask is the usual convention.
- Enter the underlying price, strike and days to expiry.
- Enter the risk-free rate and any dividend yield.
- Read the implied volatility, then the implied move — the expected move over the option's remaining life — which puts the figure in the underlying's own units.
- Repeat across several strikes to see the volatility smile — the pattern of different implied volatilities across the chain.
Limitations of the Implied Volatility calculator
Every calculation makes assumptions. These are the ones that matter here.
- Inherits every Black-Scholes assumption. The implied volatility is the number that makes that model fit, not a directly observed quantity.
- Different strikes and expiries imply different volatilities. There is no single implied volatility for an underlying, which is itself evidence the model's constant-volatility assumption does not hold.
- Sensitive to which price is used. Bid, mid and ask give different answers, and on illiquid options the spread can be wide enough to make the difference large.
- Deep in- and out-of-the-money options have very little time value, so a small price change moves the implied volatility a great deal.
- Uses European pricing, so implied volatility on an American option carries the early-exercise premium as extra apparent volatility.
Frequently asked questions about Implied Volatility
What does implied volatility actually mean?
It is the annualised standard deviation of returns that the option's price implies, under the model's assumptions. A 30% implied volatility means the market is pricing roughly a two-in-three chance that the underlying finishes within ±30% of its forward price a year out.
Why does an options IV calculator need the option's traded price?
Because implied volatility is not observable anywhere on a chain — it is the one term in the model that has to be inferred. Strike, expiry, spot and rate are all known, so the traded price is what the solver works backwards from. Feed it a different price and the volatility it returns changes accordingly.
Why does each strike show a different implied volatility?
That pattern is the volatility smile or skew. It exists because real returns have fatter tails and more downside jumps than the model assumes, so the market pays more for out-of-the-money puts than a constant-volatility model would suggest. The smile is the market correcting for a known limitation.
Is high implied volatility good or bad?
Neither on its own, and this calculator does not assess it. It means options are expensive relative to low-volatility periods, which matters differently to a buyer and a seller. What it does not tell you is direction.
How is the implied move calculated?
Underlying price × implied volatility × √(days ÷ 365). The square root is there because volatility scales with the square root of time, not linearly — which is why a 30-day option implies far less than a twelfth of the annual figure. The expected move calculator runs the same arithmetic when you already have a volatility figure to hand.
Why use bisection rather than a faster method?
Because it always converges. Newton-Raphson divides by vega, which approaches zero for deep in- and out-of-the-money options — exactly the cases where it then produces an enormous step and diverges. Bisection is slower per iteration and never fails.
Last reviewed . See our methodology and editorial policy.
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