Implied volatility explained

Implied volatility (IV) is the volatility you would have to put into an option-pricing model, such as Black–Scholes, for the model’s price to equal the option’s market price. The Options Industry Council describes it as a measure of how much the marketplace expects the price to move, based on the option’s price. It is quoted as an annual percentage and says nothing about direction.

Updated October 2026

Implied versus historical volatility

OIC distinguishes two kinds. Historical, or statistical, volatility measures how much the stock’s price actually changed over a past period, as the annualized standard deviation of its daily price changes. Implied volatility is read from option prices instead: it is the volatility the market implies. One looks back at what happened; the other is the price of expected movement today.

How implied volatility is solved

There is no formula that solves Black–Scholes for volatility directly. But the model’s price rises steadily as volatility rises (its vega is positive), so for a given market price there is only one volatility that fits, and a computer can search for it.

Take the call from the Greeks guide: stock $100, strike $100, six months to expiry, rate 5%, no dividends. At 20% volatility the model prices it at $6.89. Suppose it trades at $7.50. Halving the search range each time (bisection):

Keep going and it settles at 22.23%. Newton’s method gets there faster by using vega as the slope: from 20%, one step of 20% + (7.50 − 6.8887) ÷ 27.36 lands at 22.234%, and a second step at 22.231%. (Vega is used here per 1.00 of volatility.)

What the number means

IV is annualized. To turn it into a rough one-standard-deviation price range over a shorter period, multiply by the stock price and the square root of the time in years:

move ≈ S × σ × √T

At 22.23% for 30 days, that is $100 × 0.2223 × √(30/365) ≈ $6.37, so the option prices in a typical move of about $6.37 either way over the month. It is a model’s estimate of size, not a forecast of direction.

Implied volatility and price

Higher implied volatility means higher option prices, for calls and puts alike, and vega says by how much: OIC defines vega as the change in option value for a 1% change in volatility. In the example, vega is about $0.27 per point, so if IV rose from 20% to 21% with nothing else changing, the call would gain about $0.27.

Things to keep in mind

• It depends on the model. Change the model or its inputs, such as the interest rate or expected dividends, and the implied volatility changes too. OIC notes that Black–Scholes does not perfectly describe real-world options markets.
• Each option has its own. Options on the same stock with different strikes or expiries each have their own implied volatility, solved from their own prices.
• It is not direction. A high IV says the market is pricing in bigger moves, not which way they will go.

Educational only. This is not investment advice and not a recommendation to buy or sell any security or strategy. Figures are model outputs for a made-up example, not market prices.