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.
Related or Semi-related Video
Finance: What is Volatility?77 Views
In finance allah shmoop what is volatility beta this thing
that's the symbol for volatility on the street we mean
the wall one not the mean one and it is
so commonly used that the in crowd members just say
beta when they're referring to volatility unless they're from tennessee
in which case they say you ve all y'all all
right so here's a siri's of stock prices stamped each
day that has lo ve all or low beta and
here's a siri's that has high beta dead man's pulse
versus rocky mountains Well what makes a stock volatile uncertainty
Think about it this way If everyone knew for sure
what a given stocks earnings would be for the next
ten years quarter by quarter and they also knew what
the overall markets average earnings would be in a few
other things like revenue growth and world conditions and we're
going to be war inflation there wouldn't be a lot
of guesswork The quote right unquote price today would be
thirty two dollars eighty three cents and the quote right
unquote rate of compounding would be eight percent in the
stock would slowly go up but this rate but in
non disney land riel life well nobody really knows much
of anything So stockcharts look like this and nerve endings
of wall street traders look like this Neither of them 00:01:19.771 --> [endTime] looked much like this chart So that's all you
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