Volatility Smile

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DEFINITION

A common graphical shape that results from plotting the strike price and implied volatility of a group of options with the same expiration date. The volatility smile is so named because it looks like a person smiling. The implied volatility is derived from the Black-Scholes model, and the volatility adjusts according to the option’s maturity and the extent to which it is in-the-money (moneyness).

INVESTOPEDIA EXPLAINS



Changes in an option’s strike price affect whether the option is in-the-money or out-of-the-money. The more an option is in-the-money or out-of-the-money, the greater its implied volatility becomes. The relationship between an option’s implied volatility and strike price can be seen in the graph below.

 

 



Volatility Smile

 



The volatility smile is used in the analysis of a number of investments. It cannot be directly observed in over-the-counter foreign exchange markets, though investors can use at-the-money volatility and risk data for specific currency pairs to create a volatility smile for a specific strike price. Equity derivatives show both price and volatility pairs, allowing the smile to be created relatively easily.

The volatility smile was first seen after the 1987 stock market crash, and was not present before. This may be the result in changes in investor behavior, such as a fear of another crash or black swan, as well as structural issues that go against Black-Scholes option pricing assumptions. 


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