What is a volatility smile?

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A volatility smile refers to an implied volatility curve where the options above and below the at-the-money options have higher implied volatility than options that are at-the-money. So, if you picture a graph of the implied volatility curve showing the implied volatility versus the strikes, it would look like a smile. If you are not sure what is meant by implied volatility, check out this article.

Why could there be a volatility smile instead of a flat volatility curve?

Remember the main factors that make up an option’s value:

i)    the strike price of the option relative to the price of the underlying product

ii)   the time until expiry

iii)  the volatility in the underlying product that is expected to occur during the option’s life

Now the volatility component is known as the implied volatility of the option. And for options that share the same underlying and the same expiration date, you might expect them to have the same implied volatility. After all, the implied volatility reflects how volatile the underlying product is expected to be during the option’s life and so you might expect this to apply to all options on that product expiring at the same time. If this was the case, the implied volatility curve would be flat, i.e. the implied volatility level would be the same for all the options regardless of their strikes.

With a volatility smile, this curve is not flat; it is smile-shaped. The reason is that the implied volatility does not just reflect the expected volatility of the underlying product during the option’s life. It also reflects the supply and demand for that particular option. Imagine a product trading at $100 and the $100 strike calls and puts are trading with an implied volatility of 25%. Now if there is a lot of demand for say the $95 strike puts and the $105 strike calls, then they may trade at a higher implied volatility than 25%. Perhaps both trade at 30%. This would be a volatility smile. The strikes between $95 and $100 and between $100 and $105 would probably trade somewhere between 25% and 30% implied volatility. Outside this range, the implied volatility is likely to be even higher.

In summary, a volatility smile is an implied volatility curve where options away from the at-the-money price have higher implied volatility than the at-the-money options. It reflects the heightened demand for these options relative to the at-the-money options.

 

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