Volatility smile
The volatility smile is the curve of implied volatility across strikes for one expiry. If Black-Scholes held exactly it would be flat; in practice equity index smiles slope down from low-strike puts to high-strike calls, a shape usually called a skew or smirk, and they steepen as expiry approaches.
Senzoukria · Glossary · Updated September 2026
At a glance
- Axes
- Implied volatility against strike, moneyness or delta, for one expiry
- Equity index shape
- Higher implied volatility for low strikes (put skew)
- Built from
- Out-of-the-money puts below the forward, out-of-the-money calls above
Why the curve is not flat
Black-Scholes assumes one volatility for all strikes. Markets price otherwise: returns have fat tails, index sell-offs tend to be faster than rallies, and investors pay up for downside protection. Each strike's option is therefore quoted at its own implied volatility, and plotting them against strike draws the smile. In foreign exchange the curve is often roughly symmetric, a true smile; on equity indices it is lopsided, with the put wing well above the call wing, and practitioners speak of skew or smirk.
How it is built
- Each strike is read from its out-of-the-money option, the put below the forward and the call above, because out-of-the-money prices are pure time value and usually more liquid.
- Points with no bid or a price at the minimum tick are unreliable and often dropped.
- The x-axis can be strike, percentage moneyness, log moneyness or delta; delta-based axes make expiries comparable.
- Between quoted strikes, a curve is interpolated or fitted; outside them, any value is an extrapolation.
Worked reading
Suppose a 30-day index smile quotes 22% at the strike 5% below spot, 17% at the money and 15% at the strike 5% above. The 5% out-of-the-money put costs as if the market expected 22% volatility, the call as if it expected 15%. The 7-point gap between the wings measures the slope; how far the average of the wings sits above the at-the-money level, here 1.5 points, measures the curvature. Both change over time, and both matter more for short expiries, where the same percentage distance represents more standard deviations.
In Senzoukria
The GEX module's Volatility page has an IV Smile panel with an expiration picker. It draws the implied volatility of strikes within ±5% of spot, puts below spot and calls above in two colours, with spot marked, and prints the ATM IV taken from the quoted strike closest to spot. Under the curve it prints a ±5% wing skew, the implied volatility interpolated at 95% of spot minus the one at 105%, or states that the wings fall outside the quoted range. The backend applies the same out-of-the-money rule, put below spot and call above, when it builds the smile and the implied volatility values of the Surface page.
Related
- Volatility skew
- Implied volatility (IV)
- Volatility surface
- Volatility skew explained
- Volatility: smile, term structure and skew
In the same section
- 25-delta butterfly
- Fixed-moneyness skew
- Sticky strike vs sticky delta
- Term structure
- Volatility risk premium
- Volatility sizing
- Volatility drag
- Volume at price
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Frequently asked questions
- Is the volatility smile the same as volatility skew?
- The smile is the whole curve; skew usually refers to its slope, the difference between put-side and call-side implied volatilities. Equity index smiles are dominated by skew, which is why the words are often used interchangeably.
- Why does the smile steepen for short expiries?
- A given percentage move is many more standard deviations away for a short-dated option, so the premium for crash risk shows up as a large difference in implied volatility per strike. Plotted against delta or standardized moneyness, expiries look more alike.