Implied volatility & the surface

Every input to an option's price is observable — spot, strike, time to expiry, rates — except one. You cannot look up how much the underlying is going to move. So the market works backwards: take the price the option actually trades at, and solve for the volatility that would justify it. That number is implied volatility.

IV is not a forecast of direction and it is not measured from the past. It is the market's consensus on how much the underlying will move between now and expiry, quoted as an annualised percentage. BTC at 50% IV means the market is pricing roughly a 50% annualised range — up or down is irrelevant to the number.

This is why traders say they are buying or selling volatility rather than buying or selling options. When you buy a call you are taking a view on direction and on IV, and the two can fight each other: a rally that arrives calmly can crush IV enough to leave a long call flat or losing. That sensitivity is vega, from the previous chapter.

Skew: IV across strikes

Black-Scholes assumes a single volatility for every strike. Reality disagrees. Solve for IV at each strike and you get a curve, not a flat line — that curve is the skew, the left panel in the chart above.

In equities and indices it is usually a smirk: downside puts carry a materially higher IV than upside calls. Two reasons. Crashes are faster and more correlated than rallies, so the market genuinely expects bigger moves down. And there is persistent structural demand for downside protection from people hedging portfolios — that demand has to be paid for, and it shows up as richer put IV.

Crypto is the interesting case, because the skew flips with the regime. In a drawdown BTC behaves like equities and puts bid up. In a mania, calls do — traders chase upside with leverage and the curve tilts the other way. A skew reading of −4.2 tells you puts are richer; a positive one tells you the crowd is paying up for calls. The sign is a positioning signal in its own right.

Term structure: IV across expiries

Now hold the strike fixed and walk out in time. That is the term structure, the right panel above, and it normally slopes upward — contango. Further out means more unknowns, so more implied movement.

When it inverts, pay attention. Backwardation — near-dated IV above far-dated — means the market is pricing danger right now: an imminent event, a liquidation cascade, a macro print. Front-month options get bid because the risk is immediate, not eventual. A calm market almost never looks like this, so an inverted curve is one of the cleaner stress signals available.

Event risk also shows up as a local bump rather than a smooth slope: the expiry that straddles a scheduled catalyst prints a visibly higher IV than the ones on either side of it.

The surface: both axes at once

Skew and term structure are not two separate objects. They are two cuts through the same one. Plot IV against strike and expiry together and you get the volatility surface: skew is a slice across it at fixed time, term structure is a slice along it at fixed strike.

The shape carries information no single number does. A steep wall on the low-strike, short-dated corner is the market paying up for immediate downside. A surface that is high everywhere is expensive optionality across the board. And because the surface moves in ways spot does not, it often shifts before price does — which is the whole reason to watch it.

One caution: IV is a market price, not a measurement. It tells you what other participants are willing to pay, and they can be wrong. The gap between implied and what actually happens — realised volatility — is where volatility trading lives.

Next we take gamma and aggregate it across every contract dealers hold — gamma exposure (GEX) — which is where the surface stops being a picture and starts forcing people to trade.