Implied Volatility (IV)

Implied volatility (IV) is the volatility number that, when plugged into an option pricing model, gives the option's current market price. It is not measured from past prices; it is "implied" by what traders are willing to pay. High implied volatility means options are expensive because the market expects large moves; low implied volatility means options are cheap because the market expects calm. Implied volatility is the common language of options trading: traders quote, compare and trade options in terms of it rather than dollar prices.

How it is calculated#

Option pricing models such as Black Scholes take five inputs: price, strike, time, interest rate and volatility. The first four are known. Given the option's market price, traders solve backwards for the volatility that makes the model match the price. There is no direct formula, so this is done numerically, usually with a few rounds of Newton's method. See Black-Scholes Model and try it in the Implied Volatility Calculator.

Reading implied volatility as an expected move#

Implied volatility is an annualised standard deviation of returns. To convert it to an expected move over a shorter period:

expected 1 standard deviation move ≈ price × IV × √(days / 365)

A daily version uses trading days: IV divided by √252 (about 15.9) gives the expected daily move, so an IV of 16% implies roughly a 1% daily move.

What drives implied volatility#

For stock indices, implied volatility usually rises when prices fall and falls when prices rise. This inverse relationship is one reason for the volatility skew. See Volatility Smile and Skew.

IV across strikes and expiries#

There is no single implied volatility for an underlying. Each option has its own, and together they form a smile across strikes and a term structure across expiries, combining into the volatility surface. See Volatility Surface and Volatility Term Structure.

Implied vs historical volatility#

Implied volatility has tended to be higher on average than the realised volatility that follows, especially for equity indices, a gap known as the volatility risk premium. See Historical and Realized Volatility and Theta Harvesting.

Using implied volatility#

• Judge whether options are cheap or expensive relative to history and to expected movement. See IV Rank and IV Percentile.
• Choose strategies: buy options when IV is low relative to expected moves, sell when high. See Volatility Trading.
• Size trades: use expected moves to place stops and targets.
• Read sentiment: the VIX, derived from S&P 500 option prices, is often called the market's "fear gauge". See The VIX.

Common mistakes#

• Treating IV as a prediction of direction. It measures expected size of moves, not direction.
• Comparing IV across very different assets without context.
• Ignoring events that explain unusually high IV.

Frequently asked questions#

What is implied volatility?#

The volatility value that makes an option pricing model match the option's market price, representing the market's expectation of future price movement.

Is high implied volatility good or bad?#

Neither. It means options are expensive, which favours sellers if moves turn out smaller than expected and buyers if moves turn out larger.

How do I convert implied volatility to an expected move?#

Multiply the price by implied volatility and by the square root of the number of days divided by 365.

Next, compare it with what actually happened in Historical and Realized Volatility.