What Is Implied Volatility? IV vs Historical Volatility
Reviewed by Leon Moyer - Published October 9, 2026 - Last reviewed October 9, 2026
In this lesson
Explain what implied volatility measures, convert an IV into a one-standard-deviation move in dollars, and tell implied volatility apart from historical volatility.
Implied volatility (IV) is the annualized volatility inferred from an option's market price using a pricing model. It describes the magnitude of movement priced into that option, not a guaranteed move or its direction. Holding other inputs fixed, higher IV raises the model price of both calls and puts.
How Options Are Priced introduced the pricing inputs. Once the other inputs and assumptions are specified, implied volatility is inferred from the market price, and its level helps explain why otherwise comparable option premiums differ.
What does implied volatility mean in options?
Volatility measures how much a price swings. A stock that often moves 3% in a day is more volatile than one that rarely moves 1%. Implied volatility is the market's forward-looking version: how volatile traders collectively expect the stock to be between now and expiration.
It is called implied because nobody announces it. It is implied by what people are willing to pay for options. When traders expect big news, they bid option prices up, and the implied volatility rises with them.
Two things implied volatility does not tell you:
- Direction. It estimates the size of a likely move, not whether it will be up or down.
- Certainty. It is a price-based estimate, not a forecast that has to come true. Stocks regularly move more or less than their options implied.
How is implied volatility calculated?
A pricing model normally turns volatility into a price. Implied volatility runs the model backward: start from the price the market is paying and find the volatility that produces it.
Implied volatility runs the pricing model backward
Known inputs
XYZ $50, 50 call, 30 days, 4.5% rate
Market price
The call trades at $2.40
Implied volatility
About 40%: the only volatility that gives $2.40
Worked example
Backing implied volatility out of a call's price
XYZ trades at $50. A 50 call with 30 days to expiration trades at $2.40 per share. The interest rate is 4.5% and XYZ pays no dividend.
Price that call with the Black-Scholes model at different volatilities, holding everything else fixed:
The market price of $2.40 sits just above the 40% row. Solving exactly, the volatility that gives $2.40 is about 40.4%. That is the call's implied volatility. Your broker's options chain runs this calculation for every contract and shows the result in an IV column.
Illustrative and hypothetical. The ticker and prices are invented for teaching, and the figures exclude commissions, fees, margin interest and taxes, which reduce real results. Past or hypothetical outcomes do not indicate future results.
The same call at different implied volatilities
Model price per contract
Notice how evenly the price climbs: for this at-the-money call, each extra 10 points of implied volatility adds about $0.57 per share. Vega measures how much an option's model price changes for a one-point change in implied volatility, with other inputs held fixed.
What does an IV of 30% mean in dollars?
Implied volatility is quoted per year, which makes it hard to picture. A common rule of thumb converts it into a model-based, one-standard-deviation move over any number of days. The OIC's summary of standard deviation and expected moves builds the same estimate from implied volatility, the stock price and the square root of time.
In one sentence: approximate one-standard-deviation move = stock price x implied volatility x the square root of (days to expiration / 365).
For XYZ at $50 with 30% IV and 30 days left: $50 x 0.30 x the square root of (30 / 365) = about $4.30. This gives a rough range of $45.70 to $54.30. A normal-distribution approximation puts about 68% of outcomes within one standard deviation, but this symmetric dollar range is not an exact Black-Scholes probability interval or a reliable real-world odds forecast. Black-Scholes models log returns, and actual markets can jump and have heavier tails. The free profit calculator shows this figure in its Expected Move (1σ) readout. The Advanced Strategies course's earnings lessons use the at-the-money straddle price as the expected move instead, which comes out somewhat smaller.
IV also includes demand for protection and compensation for risk. It can differ across strikes and expirations on the same stock, so there is no single IV that describes every contract. Cboe discusses this volatility risk premium.
How does implied volatility differ from historical volatility?
Historical volatility (HV), also called realized volatility, measures how much the stock actually moved in the past. Implied volatility is what the options market expects from here on.
Historical volatility is calculated from past closing prices. In one sentence: historical volatility = the standard deviation of daily returns (commonly log returns) x the square root of 252, the approximate number of trading days in a year.
Worked example
Comparing historical and implied volatility
Over the past month, XYZ's daily moves have had a standard deviation of 1.5%. Annualized, that is 1.5% x the square root of 252 = about 23.8% historical volatility.
The 30-day XYZ 50 call from the example above implies about 40% volatility.
The gap says that this option prices in more volatility than XYZ has recently delivered. It does not establish that the option is mispriced: earnings or another event before expiration could change future movement.
Illustrative and hypothetical. The ticker and prices are invented for teaching, and the figures exclude commissions, fees, margin interest and taxes, which reduce real results. Past or hypothetical outcomes do not indicate future results.
Neither number is the right one. Historical volatility is a fact about the past; implied volatility is a price for the future. Traders compare them to judge whether options look expensive or cheap relative to how the stock has been behaving. IV Crush covers what happens to that gap once the event passes.
The best-known implied volatility figure is the Cboe Volatility Index (VIX), which Cboe describes as a measure of market expectations of near-term volatility conveyed by S&P 500 Index option prices.
Check your understanding
If traders suddenly expect a stock to make much bigger moves, what happens to the implied volatility and prices of its options?
Show answer
Implied volatility rises, and both call and put prices rise with it.
A $100 stock has an implied volatility of 20% and an option with 365 days to expiration. What is the one-standard-deviation expected move?
Show answer
$100 x 0.20 x the square root of (365 / 365) = $20, so roughly $80 to $120 over the year by this rule of thumb.
What is the key difference between implied and historical volatility?
Show answer
Historical volatility measures how much the stock has actually moved in the past. Implied volatility is the market's expectation of future movement, read from current option prices.
Key takeaways
- Implied volatility is annualized volatility inferred from an option's market price using a pricing model; it is not a guaranteed future move.
- It is found by running a pricing model backward from the market price.
- Approximate one-standard-deviation move = stock price x IV x the square root of (days / 365), a model-based range rather than a guaranteed outcome.
- Historical volatility looks back at actual moves; implied volatility looks forward. Comparing the two shows whether options are pricing in more or less movement than the stock has recently delivered.
Common questions
How is implied volatility calculated?
By running a pricing model such as Black-Scholes backward. Stock price, strike and time are observed, and interest rates and dividends are specified, so traders search for the one volatility figure that makes the model's price equal the option's market price. Brokers and platforms do this for you.
What is a good implied volatility for options?
There is no single good number, because normal levels differ from stock to stock. A 40% IV is high for a large, steady company and low for a volatile small one. Compare a stock's IV with its own past range, which is what IV rank and IV percentile do.
Is high implied volatility good or bad?
It depends on which side you are on. High implied volatility raises premiums, all else equal. Buyers pay more and sellers collect more, but larger potential moves can also mean larger losses for sellers. A rise in IV benefits an existing long option, all else equal. It also signals that the market expects bigger moves, in either direction.
Does implied volatility predict direction?
No. Implied volatility estimates the size of a likely move, not its direction. A stock with high IV is expected to move a lot, but the options market is not saying whether that move will be up or down.