Implied volatility

An annualised percentage, and the only input to a standard option pricing model that cannot be observed. The strike, the price of the underlying, the time left to expiry and the interest rate are all known, so a model given a volatility figure returns a price. Implied volatility runs that machinery backwards: the volatility input is varied until the model's output matches the price the option is actually trading at, and the figure that does it is the implied volatility of that option.

It is therefore a quoted opinion rather than a measurement. Historical volatility is arithmetic over prices that already exist and can only be calculated one way. Implied volatility is whatever the participants in that option are collectively willing to pay, which is why it rises before a scheduled event and falls once the event has passed even when the underlying has barely moved. It is also directionless: it states an expected size of movement and says nothing about which way, so a high figure is consistent with both outcomes.

The usual trap is the definite article. One underlying has many implied volatilities at once, one for every strike and every expiry, and they are not equal: plotted across strikes they form the smile or skew, which on equity indices is persistently tilted toward lower strikes. Any single quoted figure is therefore a convention about which options to read and how to weight them, and different conventions give different answers. A published volatility index is one such convention, built on near dated options on an index rather than on the index itself.