Lesson 14 of 25 · 6 min

The surface, and what a skew is measuring

Track 3 described the shape; the slope of it has a number, and a model reading a different column produces a different lending value.

Track 3 lesson 10 established that implied volatility differs at every strike and that the tilt in equities is called skew. This lesson puts a number on the tilt and then asks which number a collateral model should take, because the two questions turn out to be the same question.

Take an illustrative single expiry: the 90 strike implies 31.6 percent, the 95 strike 27.9 percent, the 100 strike 24.9 percent, the 105 strike 23.4 percent and the 110 strike 22.7 percent. The most common way to compress that into one figure is the spread between a downside and an upside strike. Here 31.6 minus 22.7 is 8.9 points across twenty percent of spot, which is 0.445 points of implied volatility per one percent of strike.

What the slope measures is worth stating precisely, because it is easy to confuse with width. It is the extra amount paid for outcomes below the current price relative to outcomes above it. It is a measurement of asymmetry in the priced distribution, not of how wide that distribution is. The at-the-money figure measures width; the slope measures lean.

Now the landing. A collateral model needs one volatility figure, and the surface offers five. Take $1,465,000 of market value, a 3.5 coverage multiple and a 15-session exit. Reading the 100 strike gives a 21.26 percent haircut and a lending value of $1,153,505.51. Reading the 90 strike gives 26.98 percent and $1,069,689.72. The difference is $83,815.79 of borrowing capacity, produced entirely by which column a model was built to read.

The event a haircut is sized against is a fall, and the 90 strike is where the market prices falls. A model anchored at the money is using the cheapest point on the surface to buffer against the expensive one.

Key terms

Skew slope: The change in implied volatility per unit of strike, usually quoted as the spread between a downside and an upside strike. The quantified version of the tilt.
At-the-money reference: The implied volatility at the strike nearest the current price. The conventional single summary of a surface, and the one that ignores the tilt.
Downside strike: A strike below the current price. Where the market prices declines, and therefore where the move a collateral discount is built for is actually quoted.

Worked example

Five columns, five haircuts, one holding

One illustrative expiry on $1,465,000 of market value. Coverage multiple 3.5, assumed exit 15 sessions.

90 strike, 31.6% implied: Haircut 26.98%
95 strike, 27.9% implied: Haircut 23.82%
100 strike, 24.9% implied: Haircut 21.26%
110 strike, 22.7% implied: Haircut 19.38%
Skew slope: 0.445 points per 1% of strike
Lending value difference, 90 against 100: $83,815.79

A 5.72-point difference in haircut and $83,815.79 of capacity, decided by a choice of column that appears in no agreement.

Check yourself

On one expiry the 90 strike implies 31.6 percent and the 110 strike implies 22.7 percent. What is the skew slope, and what would reading the 90 strike instead of the 100 strike do to a haircut?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.