Implied volatility calculator
Type a bid and an ask and this backs out the volatility the price implies, then tells you how much to trust it: the band the two sides of the quote span, and how many volatility points one price increment is worth.
Worked example — A $3.00 bid, $3.05 ask on a 30-day at-the-money call implies: 25.6%. Bid to ask spans 0.4 volatility points, so the true answer is a range, not a decimal.
At the money, penny wide: Healthy vega: the quote pins implied volatility to a fraction of a point.
Solver settings and skew 5
The quote $3.00 at $3.05 is consistent with anything from 25.4% to 25.8%.
One $0.01 price increment moves the answer by 0.09 volatility points. This quote pins implied volatility tightly. The number is worth comparing across strikes.
European Black-Scholes with a continuous dividend yield, solved on the price you type. No quote, chain, or venue data is read anywhere on this page. The solver brackets sigma between 0.0001% and 500% and converges the price to 1e-10.
Add a second strike above to see the skew between two points.
The no-arbitrage window comes first
A call has to price between $0.21 and $99.88 on these inputs. Outside that there is no volatility that reproduces the price, at any level.
Why the bracket matters
Newton's method divides by vega. Deep in or far out of the money, vega is close to zero, so an unguarded step lands anywhere. Every evaluation here also tightens a bisection bracket, and the moment vega drops below 1e-8 or a step leaves the bracket, the bisection takes over.
False precision is the real failure
At this strike a single $0.01 increment is worth 0.09 volatility points, so the table above prints two decimals rather than a precision the quote does not contain.
What each side of the quote implies
| Price used | Dollars | Implied volatility |
|---|---|---|
| Bid | $3.00 | 25.39% |
| Mid | $3.03 | 25.61% |
| Ask | $3.05 | 25.83% |
Is implied volatility the same at the bid and the ask?
No. On the default quote, the bid implies 25.39% and the ask implies 25.83%, a band of 0.44 volatility points. A single posted implied volatility number is always a point estimate inside that range, and the range is the honest answer whenever vega is small.
Three worked examples: tight, deep, and wide quotes
| Example | Quote | Implied volatility, mid | Band width |
|---|---|---|---|
| At the money, penny wide | $3.00 / $3.05 | 25.61% | 0.44 pts |
| Deep in the money | $30.15 / $30.35 | 63.81% | 16.10 pts |
| Wide market, far out of the money | $0.20 / $0.40 | 46.49% | 6.33 pts |
How the solve works
Seeded by the Brenner-Subrahmanyam approximation, solved by a Newton step bracketed inside a tightening bisection so it cannot run away when vega collapses, and converged on price to 1e-10.
This is a European model, so American options with early exercise value will imply slightly high. One volatility is solved per strike and per expiry: real markets have a surface, and the second-strike field shows how much it tilts between two points rather than fitting it. Discrete dividends are approximated by a continuous yield, and nothing here reads a chain or a venue: every input is typed. To price an option from a volatility you supply, use the Black-Scholes calculator; to turn the answer into a range and a probability, use the expected move calculator.
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What Pro adds here
A full smile fit across strikes, a term structure view, and American-style implied volatility on a binomial tree are Pro features. The launch list sends one email at launch.