Implied volatility is the price

Black-Scholes takes six inputs: spot, strike, time, rate, carry and volatility. Five of those are observable. Volatility is not — nobody knows what the future holds.

So the market inverts the problem. It quotes a price, and you solve backwards for the volatility that price implies. That number is implied volatility, and it is the only genuinely negotiable input. Everything else is arithmetic.

Options are quoted in volatility

On a professional desk, options are not really priced in currency. They are priced in vol, and the currency figure falls out at the end. Two options on different underlyings at different strikes with different premiums are directly comparable once expressed as implied volatility — which is the whole reason the convention exists.

When someone says an option "looks expensive", they almost never mean the premium. They mean the implied volatility is high relative to what they expect the underlying to actually do.

Implied versus realised

Realised volatility is what the underlying did, measured after the fact. Implied volatility is what the market is charging for it in advance.

The gap between them is the trade. Selling options is a bet that implied exceeds realised; buying them is the reverse. Implied is usually a little higher, which is the risk premium option sellers earn — and which is also why selling volatility wins most of the time and occasionally loses catastrophically.

Move the volatility slider on that strangle. The expiry line does not budge — at expiry only the spot price matters. But the pre-expiry line moves a great deal, because the position's mark-to-market is a pure volatility view until the last day. Short volatility positions are marked against you long before they are settled against you.

The smile

Black-Scholes assumes one volatility for all strikes. The market disagrees.

Plot implied volatility against strike and you get a curve, not a line: out-of- the-money puts trade at higher implied volatility than at-the-money options, and often higher than out-of-the-money calls. The shape is called the volatility smile, or the skew when it leans one way.

It exists because the model's assumptions are wrong in a specific direction. Returns are not normally distributed; crashes are larger and more frequent than the maths allows, and they are correlated with everyone wanting protection at the same time. The smile is the market pricing in what the model leaves out.

Equity indices show a pronounced downside skew for exactly this reason. FX tends toward a more symmetric smile, because either currency can be the one that collapses.

What this means in practice

• A single volatility number for a multi-strike position, which is what this site's calculator uses, is a simplification. It is fine for understanding shape and wrong for pricing a real trade against a real surface.
• If you are quoted a price, ask what vol it implies before deciding whether it is expensive.
• If a strategy looks like free money, you are usually short a tail that is not in the model. The smile exists precisely because those tails are real.

I spent a good part of my time at Otkritie building the pricing engine that produced these curves for the desk — implied vol, the smile, and the Greeks that fall out of them, across index, commodity, FX and single-stock options. The lesson that stuck: the model is a language for expressing a view, not a source of truth. It is most dangerous when it agrees with you.