Options and volatility · O7 · 8 min

Skew and term structure

Read how implied volatility differs by strike and by expiry, and say what that shows the market fears.

In the news: “Put skew is the steepest in months”: investors paying more for protection against a fall.

The essentials

The smile: Options on one underlying trade at different implied volatilities by strike, and plotted against strike they form a curve. With an index at 100, the 90 put might trade at 24%, the 100 strike at 19% and the 110 call at 16%.
Put skew and call skew: In share indices, low-strike puts carry the highest , called : markets fall faster than they rise and investors keep buying protection. Some commodities, such as natural gas, show call skew.
Risk reversal and butterfly: The is the 25-delta call’s volatility minus the 25-delta put’s: −4 means puts trade 4 points over calls. The shows how far both wings sit above the at-the-money volatility.
Term structure: The is at-the-money volatility by expiry. It slopes upwards in calm markets and inverts in a sell-off, when near-dated volatility jumps most; a known event lifts the first expiry after it.
Volatility surface: Implied volatility by strike and expiry together: a smile for every expiry. Desks value their whole options book from the every day and watch how it shifts as markets move.

Quoting the smile

Risk reversal = σ(25Δ call) − σ(25Δ put); butterfly = ½[σ(25Δ call) + σ(25Δ put)] − σ(ATM)

σ(25Δ call): implied volatility of the 25-delta call
σ(25Δ put): implied volatility of the 25-delta put
σ(ATM): at-the-money implied volatility

All Options and volatility essentials on one page →

How it works

1. Not one volatility but many

If one model fitted every option perfectly, all options on an index would trade at the same implied volatility. They don’t. With the index at 100, the 90-strike put might trade at 24%, the 100 option at 19% and the 110 call at 16%. Plot implied volatility against strike and you get a curve, often called the smile.

2. Put skew in share indices

In share indices, low-strike puts carry the highest implied volatility: the curve leans, or has . Markets fall faster than they rise, volatility jumps in sell-offs, and investors keep buying puts as insurance, so sellers charge more for them.

3. Call skew

Some markets fear a rise instead. In natural gas or grains, a can send prices sharply higher, so high-strike calls carry the highest implied volatility: call skew. The skew points at the move the market fears.

4. The risk reversal

Traders sum up the lean with one number. Take a put and a call equally far out of the money, usually those with a delta of 0.25 (25-delta). The is the call’s implied volatility minus the put’s: −4 means puts trade 4 points above calls, so the market is paying more for protection against falls.

5. Risk reversals in currencies

Currency options use the same quote, as calls and puts on the first currency in the pair. A EUR/USD risk reversal of −1.0 means euro puts trade a point above euro calls: the market pays more to guard against a weaker euro. If it moves to +1.0, the fear has switched to a stronger euro.

6. The butterfly

A second number shows how far both ends of the curve sit above the middle: the . It is the average of the two 25-delta volatilities minus the at-the-money one. Put at 23%, call at 18%, at the money 19%: (23 + 18) ÷ 2 − 19 = 1.5.

7. Volatility by expiry

Now plot at-the-money implied volatility against expiry instead of strike: the . In calm markets it slopes upwards: near-dated volatility is low, and longer expiries price in the chance of trouble later.

8. Stress and known events

In a sell-off the term structure turns upside down: near-dated volatility jumps far more than long-dated, because the market expects the stress to fade. A known event, such as an election or company results, lifts the first expiry after it, making a bump.

9. The volatility surface

Put strike and expiry together and you have the : a smile for every expiry. Desks value their whole options book from it every day, and watch how it shifts as markets move.

Worked example

One-month index options: the 25-delta put trades at 24.5% implied volatility, at the money at 19.0% and the 25-delta call at 16.5%. A week later, after a sell-off, they are 33.0%, 27.0% and 24.0%. Three-month at-the-money volatility is now 24%.

Before: risk reversal = 16.5 − 24.5 = −8.0.
Before: butterfly = (16.5 + 24.5) ÷ 2 − 19.0 = 1.5.
After: risk reversal = 24.0 − 33.0 = −9.0.
After: butterfly = (24.0 + 33.0) ÷ 2 − 27.0 = 1.5.
At-the-money volatility rose 8 points and the skew leaned 1 point further: puts gained most.
One-month at 27% is now above three-month at 24%: the front of the term structure has inverted.

The risk reversal moves from −8.0 to −9.0 with the butterfly at 1.5: volatility higher, skew steeper and the front inverted.

Check yourself

8 quick questions on the explanation above.

Practice

New numbers every set. Misses and guesses go into your review deck.

In the interview

Answer out loud in under a minute, then compare.

Why are out-of-the-money index puts expensive?
What happens to the volatility term structure in a sell-off?
What’s a risk reversal, and what does it tell you?

Remember

Risk reversal = call vol − put vol

The smile prices the tail the market fears, and the term structure shows when: calm curves slope up, stressed ones invert.

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