What is volatility smile?

What is volatility smile?

Approach: Describe pattern of implied volatility across strikes.

Pattern where implied volatility varies with strike price, often U-shaped. For equity options, typically downward sloping (skew) due to crash fear. Suggests Black-Scholes assumption of constant volatility is wrong.

Follow-up: What causes it?

Key concepts: implied volatility, market phenomena, black-scholes limitations.