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 smiling mouth. Implied volatility rises when the underlying asset of an option is further out of the money (OTM) or in the money (ITM), compared to at the money (ATM).  

Breaking Down the Volatility Smile

Volatility smiles are created by implied volatility changing as the underlying asset moves more ITM or OTM. The more an option is ITM or OTM, the greater its implied volatility becomes. Implied volatility tends to be lowest with ATM options. 

Volatility smile in options created by implied volatility versus strike price.

The Volatility Smile Enigma

The volatility smile is not predicted by the Black-Scholes model, which is one of the main formulas used to price options and other derivatives. The Black-Scholes model predicts that the implied volatility curve is flat when plotted against varying strike prices. Based on the model, it would be expected that the implied volatility would be the same for all options expiring on the same date regardless of the strike price. Yet, in the real-world, this is not the case.

Explanations for the Volatility Smile

Volatility smiles started occurring in option pricing after the 1987 stock market crash. They were not present in U.S. markets prior, indicating a market structure more in line with what the Black-Scholes model predicts. After 1987, traders realized that extreme events could happen and markets have a significant skew. These needed to be factored into options pricing. Therefore, in the real world, implied volatility has taken on a volatility smile or volatility skew.

Also, the volatility smile's existence shows that OTM and ITM options tend to be more in demand than ATM options. This could be partially due to the reason mentioned above. Extreme events can occur causing significant price shifts in options. The potential for large shifts is factored into implied volatility.

Implications for Trading Options

Volatility smiles or skews can be seen when comparing various options with the same underlying asset, same expiration date, but different strike prices. If the implied volatility is plotted for each of the different strike prices, there tends to be a u-shape. The u-shape is not always perfectly formed as depicted in the graph. 

The implied volatility of a single option could also be plotted over time relative to the price of the underlying asset. As the price moves into or out of the money, the implied volatility points will likely take on some form of a u-shape.