Volatility is uncertainty, not direction

When equity research analysts talk about "volatile stocks", they often mean "stocks that have been falling". When derivatives traders talk about volatility, they mean something completely different.

Volatility, in the precise sense used by every option pricing model, is the magnitude of moves, regardless of direction.

A stock that goes up 5% one day, down 5% the next, up 5% the day after: highly volatile. A stock that drops 1% every day for a month: very directional, but barely volatile.

Volatility doesn't have a sign. It's an absolute scalar.

Why this matters for pricing

An option's value depends on the chance that the underlying ends up somewhere far enough from the strike for the option to be in the money. Big moves up help calls. Big moves down help puts. Either way, a wider distribution of outcomes means a higher chance of one tail being in your favor.

So volatility increases option value in both directions. A 1Y at-the-money call on a stock with 30% vol is much more valuable than the same call on a 10% vol stock — even if both are expected to drift up at the same rate.

This is also why volatility itself becomes an asset class. Traders buy and sell vol as a separate quantity, hedged against direction. A long straddle (long call + long put at the same strike) has roughly zero delta — direction cancels out — but is purely long volatility. If realized moves are larger than what implied vol priced in, the straddle wins.

The trader joke

Implied vol is what you pay; realized vol is what you live with.

Implied volis the volatility input you'd need in Black-Scholes to back out the market price of an option — nothing more, nothing less. It's a number that solves an equation. Not a forecast.

Tempting interpretations to avoid: it's notthe market's forecast of underlying volatility (it depends on strike — see the smile), and it's not the implied move needed to reach the strike (an ATM option still has non-zero IV).

Realized vol is what actuallyhappens — the standard deviation of daily returns over the contract's life.

A simple option-trading career boils down to figuring out: when is implied higher than realized (sell vol — collect premium, pay out less than it cost), and when is implied lower than realized (buy vol — pay premium, collect more in P&L over time)?

Empirically, implied is usually higher than realized — that's the variance risk premium. Vol sellers collect it for taking on tail risk. The 2018 February VIX spike (the "vol-mageddon") was an exhibit of what happens when a generation of vol-sellers all forget that the premium exists for a reason.