delost@thedelost
a 25-delta put trades at 22% implied vol. the call at the same distance trades at 15%
same index, same expiry, same distance from the money. 7 points apart
black-scholes says that gap shouldn't exist
the model assumes one volatility number for every strike
σ constant across strikes and expiries. one distribution, lognormal returns, flat surface
plot the real chain and you don't get a flat line
you get a surface. tilted, curved, repricing every second
that tilt has a name: skew
and it's the closest thing markets have to a live fear gauge
the reason it exists is structural, not a pricing error
crashes are faster and deeper than rallies. returns have fat left tails
so protection below the market costs more than the model says, because the model's normal distribution never priced the tail correctly
this wasn't always true
before october 1987 the surface was roughly flat. the crash rewrote it permanently
one event taught the entire options market that the left tail is real, and the skew has never gone away since
the measurement is simple:
skew = IV(25-delta put) − IV(25-delta call)
on the example above that's 22 − 15 = 7 points
when that spread widens, demand for downside protection is rising. someone is paying up to hedge
when it flattens, the bid for protection is fading
same index level, same price on your chart, two completely different states of institutional fear
the chart shows where price is. the surface shows what people are paying to be wrong
and the shape carries more than direction
steepness tells you how much tail risk is priced
term structure tells you whether the fear is about this week or this quarter
curvature tells you how much the market disagrees with its own base case
retail sees one implied vol number on the option they're about to buy
a desk sees a surface and trades the difference between its shape and what that shape usually looks like
every input is public. the chain lists IV at every strike and expiry
strike on one axis, expiry on another, IV on the third. the surface builds itself
black-scholes won a nobel for a formula the market has been visibly disagreeing with since 1987
the disagreement is the signal
full breakdown in the article below
