Historical vs Implied Volatility

One measures what the market did. The other measures what the market is charging to be wrong about what comes next. The gap between them is a tradeable idea.

Two numbers, two entirely different questions

Historical (realized) volatility is a measurement. Take the log returns over a window — 20 days, 90 days — compute their standard deviation, and annualise by multiplying by the square root of 252 trading days. It is arithmetic applied to the past, with no opinion in it.

Implied volatility is a price. It is the volatility figure that, fed into an options pricing model, reproduces the option's current market price. It is not measured from anything; it is extracted from what people are willing to pay.

Why they routinely disagree

Implied volatility usually sits above subsequently realized volatility. This persistent gap is the variance risk premium: option sellers take on open-ended risk and require compensation for it, so they charge more than a fair forecast would justify.

Implied volatility is also forward-looking in a way realized volatility structurally cannot be. It knows an earnings date, an election, or an FOMC meeting is coming. A backward-looking calculation only learns about the catalyst after it has passed.

What the spread between them tells you

When implied sits far above realized, options are expensive relative to recent actual movement — the market is paying up for protection or anticipating a catalyst. When implied compresses toward or below realized, options are cheap relative to how much the asset has actually been moving.

This spread is the basis of much of volatility trading, but it is not a free signal. Implied being 'too high' before a known event may be entirely rational, because the event genuinely can produce a move that recent history has not sampled.

Which to use for probability modelling

If options data is available and liquid, implied volatility is generally the better forward-looking input, because it incorporates known upcoming catalysts. Its weakness is the embedded risk premium, which biases probability estimates toward wider ranges than are strictly warranted.

Realized volatility is unbiased in that specific sense and requires no options market at all, which makes it usable across instruments where clean options data is unavailable or unreliable. Its weakness is that it is blind to the calendar ahead.

A common compromise is to blend several realized estimates over different windows — a short window for the current regime, a longer one for the baseline — and treat their agreement as a confidence signal. When the estimates cluster, the volatility regime is stable; when they diverge sharply, it is in transition and any single number should be trusted less.