Skew Risk And Smile Hedging

Plot implied volatility against strike for a fixed expiry and, for equity index options, you get a downward-sloping curve — out-of-the-money puts trade at noticeably higher implied volatility than out-of-the-money calls. That curve is called the skew, or more generally the smile, and it does not move as one block. It can shift up or down in level (all strikes get more or less volatile together), or it can steepen or flatten independently — puts getting relatively more expensive than calls even while the average stays put. A portfolio can hold zero net vega and still be fully exposed to that second kind of move.

A seesaw, not just an elevator

An elevator moves a whole floor up or down together — a level shift, the kind ordinary vega measures. A seesaw is different: one end goes up exactly as the other goes down, the middle barely moving — a skew shift, puts and calls moving in opposite directions around a stable centre. A trader who only watches average volatility (the elevator) has no instrument for detecting whether the seesaw tilted, and a portfolio can be perfectly hedged against the elevator while sitting on one end of an untethered seesaw.

Two separate risk numbers

Skew risk needs its own Greek, distinct from vega. A common construction bumps the smile's slope rather than its level: pick a benchmark low and high strike, and define

$$\text{Skew vega} \;=\; \text{vega}_{\text{put wing}} \;-\; \text{vega}_{\text{call wing}} \;\; \text{weighted by a steepening shock},$$

or more simply, a position's sensitivity to a shock that raises implied vol at the low strike and lowers it equally at the high strike, leaving the at-the-money level unchanged. In plain English: instead of "what if volatility rises everywhere," skew risk asks "what if puts get relatively more expensive and calls relatively cheaper" — a different, independently tradeable move.

Worked example 1: a risk reversal is pure skew exposure, zero vega

A risk reversal is long an out-of-the-money call and short an out-of-the-money put, roughly matched in vega so net vega is small. Say long 10 contracts of a 25-delta call, vega $0.15$ each, short 10 contracts of a 25-delta put, vega $0.16$ each.

Net (level) vega: $10(0.15) - 10(0.16) = 1.5 - 1.6 = -0.1$, close to flat.

Skew exposure: if the skew steepens by 1 point (puts get relatively 1 point more expensive, calls 1 point cheaper, level unchanged), the short put alone accounts for the move: -10 \times 0.16 \times (+1) = -\1.6$. The long call adds roughly$10 \times 0.15 \times (-1) = -$1.5$on top, since it is on the cheapening side too. Total: about$-$3.1$from a shock that "total vega" of$-0.1$ said should barely register.

Worked example 2: a butterfly's exposure to the smile's curvature

A butterfly (long a lower-strike put, short two at-the-money options, long a higher-strike call, roughly vega-neutral by construction) has almost no exposure to the skew's slope moving, but is exposed to how curved the smile is — whether the wings are getting relatively more expensive than the middle. Suppose the wings' combined vega is $0.30$ and the body's is $-0.30$, netting to zero total vega and roughly zero slope exposure. If the whole smile flattens (wings get 1 point cheaper relative to the body), the position loses about 0.30 \times (-1) = -\0.30$ from the wings, even though level and slope both read near zero. This is a third, separate risk — curvature, or "smile risk" — that a level-and-slope-only report would also miss.

The surface below is a live version of the seesaw picture above, but across both strike and tenor at once. Compare the slope at low strikes to the slope at high strikes for a single tenor — that difference is the skew a risk reversal is built to trade.

What this means in practice

Options desks trade risk reversals and butterflies specifically as tools to isolate skew and curvature risk from level risk, and any book of any real size needs a risk report that separates all three — level, slope, curvature — rather than a single vega figure, exactly the way vega bucketing separates risk by expiry instead of blending it into one number. Skew risk spikes visibly around known event dates, since demand for downside protection (puts) surges ahead of uncertain outcomes and eases once they pass.