Skew and the Smirk
Black-Scholes assumes one volatility for all strikes. Markets disagree. The shape of how IV varies across strikes encodes what people are afraid of.
The single-vol assumption was wrong
The original Black-Scholes model from 1973 assumed a single volatility for all options on the same underlying with the same expiry. Plug in σ, get out a price. Every strike was supposed to imply the same σ.
Then markets began trading. By the late 1970s, traders knew the assumption was false. By the 1987 crash, it was undeniable. Different strikes implied different vols. The shape of those differences came to be called the volatility skew or smile, depending on the underlying.
Equity skew
Index options like SPX show a clear pattern: out-of-the-money puts trade at substantially higher IVs than at-the-money options, while out-of-the-money calls trade at lower IVs. The shape slopes down from left to right. Traders call this the "equity skew" or "the smirk."
The economic story: investors want crash protection. The market for OTM puts is bid because pension funds, asset managers, and institutional holders are all buying insurance against a market crash. They are willing to pay above the statistically fair vol to get it. There is no equivalent demand for OTM calls. Few people pay for protection against a stock rally.
The result is a persistent vol surface that prices downside protection above upside speculation. The shape is structural and has been stable for decades.
FX smile
Currency options often show a more symmetric shape. Both OTM puts and OTM calls carry premium relative to ATM. The reason: currencies can move violently in either direction. A USDJPY trader needs to hedge both "yen too strong" and "yen too weak." Demand for OTM puts and OTM calls is roughly balanced.
Some single-name equity options also show smile-like behavior, especially small-caps and high-momentum names where both crashes and squeezes are real possibilities.
Why skew exists in equity options
Several explanations have been offered. They are not mutually exclusive.
- Crash risk premium. Markets jump down more often than they jump up. Options pricing reflects this. OTM puts pay off in left-tail events; their price is bid up to reflect the asymmetric risk distribution.
- Hedging demand. Long-only investors are structurally net long. Their hedging needs are concentrated in puts. The supply-demand imbalance pushes put IVs up.
- Leverage effects. When stocks fall, debt-to-equity ratios rise, which mechanically increases the volatility of the equity. Falling prices and rising vol are correlated. Options pricing reflects this correlation.
- Sentiment and overreaction. After every crash, OTM put demand spikes. Some of the skew is permanent overpricing of tail risk relative to the actuarial frequency.
How skew is measured
Several conventions exist. The most common measures are:
- 25-delta risk reversal. The IV of the 25-delta put minus the IV of the 25-delta call. Positive values indicate downside skew. SPX typically runs 4-8 vol points positive in normal markets.
- SKEW Index (CBOE). A model-based measure that rises as far-OTM puts get bid relative to ATM. Higher SKEW means the market is paying up for tail protection.
- Skew slope. Linear regression of IV against delta or log-strike. The slope quantifies the steepness of the curve.
Lesson L.21 develops the 25-delta risk reversal as a positioning signal. For now, treat skew as a measurable feature of the surface, not a vague concept.
Skew is not constant
Skew steepens during stress. When the VIX rises, the skew typically rises with it, sometimes faster. This is because OTM puts get bid first (panic hedging) before ATM IV catches up. After the storm passes, skew often relaxes faster than ATM IV does. This dynamic creates trading opportunities for traders who can decompose the surface into level and shape.
The implication for pricing
Once you accept that the vol surface is curved, Black-Scholes stops being a pricing model and becomes a quoting convention. Traders use it to translate between price and IV, but they do not believe the model's assumptions. Real pricing happens at the surface level: the vol used for pricing depends on the strike, expiry, and even the time of day.
This is why professional options traders speak in IV, not in dollar prices. The dollar price is a derived quantity. The IV (and where it sits on the surface) is the real number.
What you carry forward
- Different strikes have different IVs. The pattern is called skew (one-sided) or smile (symmetric).
- Equity index options show a strong downside skew driven by hedging demand for crash protection.
- FX options often show a more symmetric smile.
- Skew is measurable: 25-delta risk reversal, CBOE SKEW Index, slope-based measures.
- Selling skew is selling tail insurance. The premium is real; the risk is concentrated.