What Is the ‘Volatility Smile’ and How Does It Relate to Options Pricing?

The volatility smile is a pattern observed in the options market where at-the-money options have lower implied volatility than both in-the-money and out-of-the-money options with the same expiration date. It suggests that the Black-Scholes assumption of constant volatility across all strike prices is incorrect.

It is crucial for pricing because it shows the market's perception of risk is not uniform across strike prices.