Skew

Modelling and interpreting the skew is one of the key areas in equity derivatives research, as it is is probably the most distinctive feature of equity volsurfaces.

It is defined as the slope of the volsurface in the strike direction, at a given expiry (T). In detail though, there is no agreement on a unique way of computing it.

Our definition: the slope of the surface at 1 year, around the atm-forward strike.

E.g.skew = -20%
the vol changes by 20% of the difference in strike: i.e. by 2 volatility points going from 95% to 105% of the forward, at T=1year.

Observations

In equity derivatives, skew is nearly always negative. Note: This explains why the VIX goes up when the SPX goes down.

At other expiries, empirically the skew scales roughly with 1/sqrt(T) so at 4 years it is ~ half, at 3 months roughly double.

This is called the term structure of skew, and it is another hot area of research.

For example the proponents of rough-vol in 2020,2021 point out to the much slower rate of decay observed for SPX options in the very near term, while at the farther end we have often observed and reported a much faster rate of decay, e.g. on European indexes 2015 or later.

Typically, up to 2007 a skew of -25% on an index was already considered quite steep and -30% hardly ever seen. After that, -30% and steeper has been often observed. Normally, skews for stocks are flatter, and similarly for Asian indexes.

See here for some indicative current levels.

"Long skew", "short skew"

A portfolio of equity derivatives (or equivalently, structured products) is "long skew" if it's mark-to-market (or mark-to-model) value increases when the skew steepens (i.e. when it becomes more negative - sorry if it is confusing but that's how the convention is).

Examples. E.g., a collar.

Being long a vanilla option strike 90 and short another vanilla strike 110 (same maturity) will be "long skew"

Owning a knock-in put will make you long skew. Selling it, will make you short skew. Et cetera.