Implied Volatility and Realized Volatility

If you want to trade options seriously, there’s one concept you can’t skip: volatility. It’s come up in almost every post on this blog — it’s part of the premium you collect, the delta you choose, the reason one stock pays richer than another — but I’ve never stopped to properly define it. Today I want to fix that, and then go one step further, because the single most useful thing you can learn about volatility isn’t what it is — it’s that there are two different kinds, and the gap between them is where a lot of the real edge lives.

Those two kinds are implied volatility and realized volatility. Some options strategies are built almost entirely on forecasting the relationship between them — as we saw in directional vs volatility trading. So let’s define volatility once and for all, then look at both kinds.

What volatility actually is

The textbook definition sounds complicated: volatility is the annualized standard deviation of the logarithmic returns of an asset’s price. Let me break it down, one piece at a time:

• Standard deviation is just a measure of how spread out a set of numbers is around their average — how jumpy they are. Small standard deviation, everything clusters together; large one, the values are all over the place.
• Returns are the percentage changes from one day to the next. Log returns are a slightly reworked version (using the natural logarithm) that mathematicians prefer because they add up cleanly over time — but for our purposes, just read it as “daily moves.”
• Annualized means we scale that daily number up into a yearly figure, so every stock is measured on the same ruler.

Strip all of that away, and volatility is really just this: how much a stock jumps around. A calm, sleepy utility that drifts a few cents a day has low volatility. A biotech that lurches 6% in either direction on any given morning has high volatility. That’s the whole intuition.

And here’s the part beginners constantly get wrong, so I’ll put it in bold: volatility has no direction. It doesn’t care whether the stock goes up or down — only how far it travels. A day where a stock gaps +8% and a day where it gaps −8% contribute the exact same amount of volatility. It measures the size of the swing, not the sign of it.

One quick way to make the number concrete: a stock with 20% annualized volatility is expected to move roughly 1.25% on a typical day (you get that by dividing 20% by the square root of the ~252 trading days in a year). So next time you see a stock quoted at “20% IV” — really a single summary figure blended from its options — you can translate it into a real, day-to-day movement instead of an abstract percentage.

You’ll often hear volatility described as a “measure of fear.” That’s only half true — and it’s worth getting right, because the fear part really belongs to just one of the two kinds: the implied one. Plain volatility is pure magnitude. Fear only enters the picture when we start talking about what the market expects. Which is exactly where we go next.

Implied volatility: what the market expects

Implied volatility (IV) is forward-looking. It’s the market’s collective guess about how much a stock will move between now and an option’s expiration — and it’s baked right into the price of that option. When traders expect turbulence, they bid option prices up, and IV rises. When they expect calm, premiums deflate and IV falls.

That gives you a clean rule of thumb: high IV means fat, expensive premiums (the market is pricing in a big move), and low IV means thin ones (the market expects quiet). As a seller, IV is the forecast that decides how much premium you’ll collect.

Now, the slightly mind-bending part: you don’t calculate implied volatility directly — you back it out. Every other ingredient that goes into an option’s price is knowable (the stock price, the strike, the days left, interest rates). Volatility is the one thing nobody can observe. So instead of feeding volatility in to get a price, traders take the real market price and run the pricing model in reverse to solve for the only missing piece. That number — the volatility the price implies — is your IV. I broke all of this down in how options are actually priced, and if you want to see the reverse-solve happen, you can plug real numbers into our implied volatility calculator and watch it work.

That said, volatility being directionless doesn’t mean it’s uncorrelated with the underlying. With equities there’s usually an inverse correlation — prices fall, volatility rises. With oil it’s often a positive one — volatility rises as the price spikes up. Gold is usually fairly positive or flat. So volatility measures the size of a move, not its direction — but how the two relate depends on the asset.

Realized volatility: what actually happened

If implied volatility is the forecast, realized volatility (RV) is the report card. It’s backward-looking — it measures how much the stock actually ended up moving over some past window. Where IV is an expectation, RV is a fact… or at least, it looks like one.

Here’s the subtlety that trips people up. You’d assume that, being purely backward-looking, RV would be a single hard number — just measure what happened and you’re done. But it isn’t. There is no one “true” realized volatility. It’s still an estimate, because measuring it forces you to make choices: which prices do you sample — only the closing prices, or the highs and lows too? Over what window? Weighted how? Different reasonable choices spit out different numbers. That’s why there isn’t one formula for RV — there’s a whole family of them, each making a different trade-off between simplicity and how much information it gets out of the data.

The three you’ll run into most often:

• Close-to-Close (C2C) — the classic. It uses only each day’s closing price and takes the standard deviation of the daily log returns. In formula terms, annualized: σ = √( (252/N) · Σ(rᵢ − r̄)² ), where rᵢ = ln(Cᵢ / Cᵢ₋₁). It’s simple and honest, but it throws away everything that happened inside the day and reacts slowly, because it only ever “sees” the close.
• Parkinson — instead of just closes, it uses the daily high-low range, so it captures how wild the day actually got even if the stock closed flat: σ = √( (1 / 4ln2) · (1/N) · Σ ln(Hᵢ/Lᵢ)² ), annualized. It’s more efficient (more signal from the same days), but it assumes all the action happens while the market is open — so it misses overnight gaps.
• Yang-Zhang — the most complete of the common three. It stitches together the overnight move (yesterday’s close to today’s open), the intraday range, and a drift adjustment, so it handles the two things Parkinson can’t: opening gaps and trends. It’s a weighted blend of several pieces rather than a tidy one-liner — which is precisely why it’s the most robust. For most people, it’s the best off-the-shelf estimator.

If your eyes glazed over those formulas, no problem — the takeaway is the only thing you need: measuring “what actually happened” is fuzzier than it sounds, and better estimators get more accuracy out of the same price history.

Why the gap between them is the whole game

So now we have a forecast (IV) and an outcome (RV). Put them side by side and you’ve unlocked the single most important comparison in volatility trading.

Here’s the punchline, and it’s good news for option sellers: over the long run, implied volatility tends to run a little higher than the realized volatility that actually follows it. The market, on average, overpays for the fear of movement. That persistent gap even has a name — the variance risk premium — and it’s the same statistical edge I wrote about in selling vs buying options, just viewed through the volatility lens. Sellers get paid, over and over, for carrying anxiety the market would rather offload. It’s the insurance-company business model in disguise.

But to trade that gap cleanly, you run into a problem: an option’s price also moves with direction, not just volatility. If you sell an option purely to bet that IV is too rich, a hard move in the stock can bury you long before your volatility view has a chance to be right. So dedicated volatility traders strip the direction out — they hedge, continuously holding an offsetting position in the underlying stock so the trade barely cares which way the price goes. That’s the delta-neutral idea from the directional vs volatility post. What’s left, once direction is neutralised, is an almost pure bet on one question: did the market overpay for fear, or underpay? IV versus RV, and nothing else.

That fully-hedged version is an advanced game, and I’m not suggesting you run a delta-neutral book next week. But even if you never hedge a single position, the mental model is still really useful. Because every time you sell a cash-secured put, you are — whether you realise it or not — also betting that implied volatility is richer than the volatility that will actually show up. Understanding that is what turns “selling premium” from a hopeful habit into an informed decision.

Volatility isn’t the scary part of options trading. Once you can see it as two numbers — what the market fears, and what actually happens — it stops being a source of anxiety and starts being the thing you read the market with.

Happy Investing,

Francesco