Volatility Smile

When you buy an option, you can pick from a range of strike prices and a range of expiration dates. It's like picking the toppings on a pizza. You can mix 'n' match however you like.

Each option comes with a measurable amount of implied volatility. A volatility smile applies to options with the same expiration date but different strike prices. It relates to the shape made by graphing the implied volatility. The measure gets higher the further away the strike price gets from the current trading price for an asset. If a stock is trading at $20, implied volatility for the $20 strike price will be low. However, the further away from the current price you go (in either direction), the higher implied volatility gets.

So...with the stock trading at $20, the $15 strike price will have higher volatility than the $18 strike price. Meanwhile, the $25 strike price will have higher implied volatility than the $22 strike price. And $18 and $22 strike prices will have similar implied volatility.

The implied volatility here applies to the options themselves, rather than the underlying asset (like a stock). The prices for the options themselves are more likely to move around; that's because demand is higher for options further in-the-money or further out-of-the-money than it is for options closer to the at-the-money level.

Graph the IV for all strike prices for the same underlying asset and the same expiration date, and the graph will look like a smile. It's not true for all options, but it does hold for most. This situation comes as options show high levels of implied volatility for both extreme in-the-money options and extreme out-of-the-money ones. Meanwhile, IV is low for at-the-money options. The extremes are high...the middle is low. Like a smile. Ish.