What Is the Volatility Smile?
The volatility smile is a graphical pattern showing how implied volatility varies across different strike prices for options with the same expiration date. When plotted, IV forms a U-shaped curve (smile) or an asymmetric curve (smirk/skew). In the Black-Scholes model, IV should be constant across all strikes. The fact that it is not reveals important information about how the market actually prices risk versus the model's assumptions.
The volatility smile tells us that the market assigns higher probabilities to extreme price moves (both up and down) than a normal distribution would predict. This is because real stock returns have 'fat tails': large moves occur more frequently than the bell curve suggests. The market compensates for this by pricing OTM options higher than the Black-Scholes model would, creating the smile pattern.
A true smile is U-shaped (both wings elevated). A smirk or skew is asymmetric (one wing higher than the other). In equities, the left wing (puts) is typically higher, creating a smirk. In FX, a true smile is more common. The shape reveals the market's asymmetric view of upside vs. downside risk.
Anatomy of the Volatility Smile
| Strike | Delta | Moneyness | Typical IV | vs. ATM |
|---|---|---|---|---|
| $80 | 0.05 (deep OTM put call) | 20% OTM | 40% | +10% |
| $90 | 0.25 (OTM put call) | 10% OTM | 35% | +5% |
| $95 | 0.40 | 5% OTM | 32% | +2% |
| $100 | 0.50 (ATM) | ATM | 30% | Baseline |
| $105 | 0.40 | 5% OTM call | 28% | -2% |
| $110 | 0.25 (OTM call) | 10% OTM | 28% | -2% |
| $120 | 0.05 (deep OTM call) | 20% OTM | 32% | +2% |
- 1Left wing steepness = (40% - 30%) / 20% moneyness = 0.50 per % OTM
- 2Right wing steepness = (32% - 30%) / 20% moneyness = 0.10 per % OTM
- 3Smile width = avg(40%, 32%) - 30% = 36% - 30% = 6%
- 4Skew = 35% - 28% = 7% (significant negative skew)
- 5Shape: Asymmetric smirk (left wing much steeper)
- 6The market prices crash risk 5x more aggressively than rally risk
Why the Smile Matters
Using the Volatility Smile
- The smile reveals that Black-Scholes assumption of constant volatility is wrong
- Fat tails in real return distributions create the smile shape
- The smile emerged after the 1987 crash and has persisted ever since
- Different asset classes have different smile shapes
- Stochastic volatility models (Heston, SABR) attempt to capture the smile
The smile shape changes over time. During market stress, the smile steepens (wings rise relative to ATM). During calm periods, it flattens. Trading smile dynamics involves buying options when the smile is unusually flat and selling when it is unusually steep, relative to historical norms.
The volatility smile is evidence that the Black-Scholes model is a simplification. More advanced models like the Heston stochastic volatility model, local volatility models, and jump-diffusion models were developed specifically to capture the smile shape and price exotic options more accurately.