Skew

Pull up one expiration on SPY and read the IV column down the puts. The strikes below the market carry a higher implied volatility than the strike at the money, and the further down you go, the higher it gets. Now walk up the call side and the numbers fall. Same stock, same expiration, and yet a different price of volatility at every strike. That tilt is called skew, and it decides what every spread you will ever trade costs.

Why the puts cost more

Two things push the downside up. The first is demand. Funds that own stock buy out-of-the-money puts as crash insurance, and there is a steady bid for them in all weather. The second is supply. The market makers who sell those puts end up carrying a book of short puts, and the more they hold, the more they charge to add to it. Underneath both sits a plain fact about stocks: they fall faster than they rise, and volatility jumps when they fall. A put that pays off in a crash is worth more than a world of one flat volatility would say, and the market prices it that way.

There is a model point hiding here too. The pricing model from Module 3 assumes one volatility and a bell-shaped spread of outcomes. Real returns have fatter tails than the bell, and on stocks the fat tail is on the downside. The model cannot hold that shape, so the market bends the one input it can bend: it quotes a higher volatility for the strikes that sit out in the fat tail. Skew is the market correcting the model, strike by strike.

Smirk and smile

Plot IV against strike and the shape has a name. On SPY the curve is lopsided: steep on the put side, still falling on the call side. That one-sided tilt is a smirk. On a single stock the call wing lifts too. A stock that can gap up on a product launch or a takeover has buyers for upside calls, so both wings sit above the middle and the curve looks more like a true smile. The bigger the story around a stock, the more symmetric the smile.

Two dials describe almost every smile you will see: how hard it tilts, and how much it curls up at both ends. An index is mostly tilt. A takeover candidate or a meme stock has more curl, and on a stock with a hot upside the tilt can even turn the other way.

How it is measured

Traders quote skew as the IV of the 25-delta put minus the IV of the 25-delta call, in volatility points. Using delta rather than dollar strikes keeps the number comparable across stocks and across time. Say the 25-delta put on an index shows 19% and the 25-delta call shows 13%. The skew is 6 points. On a calm day for a big index that is normal; in a sell-off it can double. Some panels quote the same thing the other way round, call minus put, so a negative figure there means the puts are the expensive side, exactly as usual.

What skew does to the price of a put

A few vol points sound small. On an out-of-the-money put they are not, because a cheap option's value is almost all volatility. Price a 30-day put 10% out of the money at a flat 25% and it is worth about 19 cents. Give it the 29% or so that a normal smirk hands that strike and it is worth about 37 cents, nearly double. Go 15% out and the gap is about five times.

Module 9 showed what the tilt does to a spread: the lower strike carries the higher vol, so a long put spread costs less than one flat vol says and a short put spread pays less. The same tilt makes a put ratio spread, selling two lower puts against one higher one, richer to put on. Ignore skew and every downside structure you price will be wrong in the same direction.

Your turn

Open the SPY chain, find the strike where the put delta is closest to minus 0.25 and the one where the call delta is closest to 0.25, and read the IV at each. Then open IV Intelligence for TSLA and read its skew figure off the strip at the top.