## What is a 'Volatility Smile'

A volatility smile is a common graph 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).

## BREAKING DOWN 'Volatility Smile'

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.

## The Volatility Smile Enigma

The volatility smile is peculiar because it is not predicted by the Black-Scholes model, which is used to price options and other derivatives. The Black-Scholes model predicts that the implied volatility curve is flat when plotted against the strike price. It would be expected that the implied volatility would be the same for all options expiring on the same date regardless of strike price.

## Explanations for Volatility Smile

There are several explanations for the volatility smile. The volatility smile may be explained by investor demand for options of the same expiration date but disparate strike prices. In-the-money and out-of-the-money options are usually more desired by investors than at-the-money options. As the price of an option increases all else equal, the implied volatility of the underlying asset increases. Because increased demand bids the prices of such options up, the implied volatility for those options seem to be higher. Another explanation for the enigmatic strike price-implied volatility paradigm is that options with strike prices increasingly farther from the spot price of the underlying asset account for extreme market moves or black swan events. Such events are characterized by extreme volatility and increase the price of an option.

## Implications for Investing

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 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 it 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.