Every option price contains a forecast, whether the person buying it realizes it or not. Baked into that price is a number called implied volatility — the market's collective guess at how much a stock is about to move. It's easy to confuse with a second, entirely different number: realized volatility, which measures how much the stock actually moved, after the fact. Traders who understand the difference between the two aren't predicting the market any better than anyone else. They're finding a mispricing between what people expected and what happened, and trading that gap directly.
What implied volatility actually measures
Implied volatility isn't observed directly — it's reverse-engineered. Options are priced using models like Black-Scholes, which take a stock's price, the option's strike price, time to expiration, and the prevailing risk-free interest rate, and combine them with one more input: expected volatility. Trading desks don't plug in a volatility guess and get a price out; they do the opposite. They take the option's actual market price, set by whatever buyers and sellers are paying for it right now, and solve backward for the volatility figure that would justify that price, testing different values until the model's output matches the market. That backed-out number is implied volatility. It's less a prediction than a mirror: a direct readout of how nervous or calm option buyers currently are, expressed in percentage terms rather than headlines.
This is the exact same math behind the VIX, which is nothing more than the implied volatility of S&P 500 index options, averaged across a 30-day window and expressed as an annualized number. A single stock carries its own implied volatility the same way the index does — it just moves for company-specific reasons instead of macro ones, and it tends to spike hardest right before scheduled events like earnings, when the market knows something is coming but not yet what.
What realized volatility actually measures
Realized volatility is the more straightforward of the two, because it doesn't require a pricing model at all — just a stopwatch pointed backward. It's calculated from a stock's actual daily returns, typically measured as log returns: the natural log of today's price divided by yesterday's, which compounds more cleanly than simple percentage change over multi-day periods. Take the standard deviation of those daily log returns over whatever window you're measuring, then scale it by the square root of 252, the number of trading days in a year, to annualize it. The output is a single percentage describing how much the stock actually swung, on average, once the dust had settled. There's no forecasting involved. Realized volatility can only ever tell you what already happened, which is exactly why it needs implied volatility's forward-looking counterpart to be useful for anything more than a history lesson.
The trade hiding in the gap between them
Once both numbers exist side by side, the trade becomes obvious. If implied volatility is priced higher than realized volatility ends up being, the options were overpriced relative to how calm the stock actually turned out to be, and sellers of those options collect the difference. If realized volatility outruns what was implied — the stock moves more violently than anyone priced in — buyers of the options come out ahead instead. Every options trade is, underneath whatever specific strategy wraps around it, a bet on which side of that gap the market got wrong.
The clearest real-world version of this shows up around earnings. In the days before a company like Apple reports, implied volatility climbs steadily as the market prices in uncertainty about a number nobody outside the company actually knows yet. The moment the report is released, that uncertainty disappears in an instant — the news is now public, whatever it is — and implied volatility collapses just as fast, often within minutes, regardless of which direction the stock moves. Options traders call this an IV crush, and it's the reason a trader can be completely right about a stock's direction after earnings and still lose money on the position: the premium was priced for the uncertainty, and the uncertainty is the thing that just evaporated.
Implied volatility prices in the unknown. Realized volatility is the bill that comes due once the unknown becomes known — and the gap between the two is the only thing volatility traders are ever actually trading.
The math looks intimidating from the outside. The idea underneath it isn't: one number is a guess, the other is a receipt, and the money gets made in the space where the guess turns out to be wrong.