Calculators
Implied Volatility Solver
Enter an option's market price and work backwards to the volatility the market is pricing in, the number options traders actually trade.
Model price vs. volatility
Implied volatility is the volatility number you have to plug into Black-Scholes to make its price match the option's actual market price, read it off the chart as the point where the rising model curve crosses the market-price line. Because that curve is upward-sloping, there is exactly one volatility that fits, and this tool finds it by inverting the formula. Traders quote and think in vol rather than raw dollars because it is far more comparable across strikes and expiry dates. A higher implied volatility simply means the market is pricing in bigger expected moves in the underlying.
Learn how it works
Five worked examples. Read a couple before you dive in, try to answer first, then reveal the solution.
The anchor: a $10.45 price implies 20% vol
A 1-year, $100-strike call on a $100 stock (r = 5%) trades at a market price of $10.45. What volatility makes Black-Scholes match that price? This is the reverse of pricing: we know the price and solve for σ.
Show solution
Implied volatility ≈ 20%.
Black-Scholes with σ = 20% produces exactly $10.45 for these inputs, so a $10.45 market price implies the market is expecting about 20% volatility over the year. There is no clean algebra shortcut, the solver just tries volatilities until the model price matches the market price. Because a higher σ always gives a higher call price, that search is quick and reliable.
Higher price, higher implied vol
The same option (S = $100, K = $100, T = 1, r = 5%) now trades at $14.20. What is the implied volatility?
Show solution
Implied volatility ≈ 30%.
At σ = 30% Black-Scholes prices this call near $14.23, essentially the market price. A richer premium means traders are paying up for a wider range of possible outcomes, so implied vol has climbed from 20% to about 30%. Price up → implied vol up, always.
Lower price, lower implied vol
The same call (S = $100, K = $100, T = 1, r = 5%) trades at only $6.90. What is the implied volatility?
Show solution
Implied volatility ≈ 10%.
A cheaper option means the market expects calmer conditions. Black-Scholes with σ ≈ 10% prices this call right around $6.80–$6.90, so the implied vol works out near 10%, well below the 20% anchor. Less expected movement → smaller option premium.
Why traders quote volatility, not price
Two options on different stocks and strikes carry very different dollar prices. Why do options traders talk in terms of implied volatility instead of the raw premium?
Show solution
Dollar prices are not comparable across strikes, expiries, and stocks, a $2 option and a $40 option can reflect the same expectations or wildly different ones. Implied volatility strips all that out and puts every option on one common scale: the market's expected annualized movement of the underlying.
Quoting in vol lets traders line up a cheap short-dated option against an expensive long-dated one, spot which strikes look relatively rich or cheap (the volatility smile), and hedge in consistent units. Price is what you pay; implied vol is what you are really trading.
A price below intrinsic value has no solution
An in-the-money call has $12 of intrinsic value (stock $112, strike $100), but someone quotes it at $11. What implied volatility does that imply?
Show solution
None, there is no valid implied volatility.
An option is worth at least its intrinsic value; here that floor is $112 − $100 = $12. A quote of $11 sits below the floor, and no volatility, not even 0%, can push the Black-Scholes price that low (raising σ only makes an option worth more, never less).
A sub-intrinsic price is pure arbitrage: buy the call at $11, exercise it to buy the stock at $100 and sell at $112, and bank the difference risk-free. Because it violates the no-arbitrage floor, the solver simply returns no solution.
What you'll learn
What implied volatility is, why traders quote options in vol rather than price, and how it's backed out of a market price.