A smile of volatility is a geographic model of implied volatility for a series of options with the same expiration date. When plotted against strike prices, these implied volatilities can create a line that rises at either end; hence the term “smile”. Volatility smiles should never occur based on standard Black-Scholes option theory, which normally requires a completely flat volatility curve. The first noticeable volatility smile was seen after the 1987 stock Exchange crash.

The option prices is more complicated than the price of stocks or commodities, and this is well reflected in a smile of volatility. Three main factors make up the value of an option: exercise price compared to the underlying asset; the time until expiration, or expiration; and the expected volatility of the underlying asset over the life of the option. Most option valuations are based on the concept of implied volatility, which assumes that the same level of volatility exists for all options on the same asset with the same expiration.

Several hypotheses explain the existence of volatility smiles. The simplest and most obvious explanation is that demand is greater for in-the-money or out-of-the-money options than for at-the-money options. Others suggest that better-developed options models led to out-of-the-money options becoming more expensive to account for the risk of an extreme stock market crash or black swans. This calls into question any investment strategy that relies too heavily on the implied volatility of the Black–Scholes modelespecially with the Evaluation downside puts that are far from the money.

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