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 underlying asset and 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). The volatility smile does not apply to all options.

Key Takeaways

  • When options with the same expiration date and the same underlying asset, but different strike prices, are graphed for implied volatility the tendency is for that graph to show a smile.
  • The smile shows that the options that are furthest in- or out-of-the-money have the highest implied volatility.
  • Options with the lowest implied volatility have strike prices at- or near-the-money.
  • Not all options will have an implied volatility smile. Near-term equity options and currency-related options are more likely to have a volatility smile.
  • A single option's implied volatility may also follow the volatility smile as it moves more ITM or OTM.
  • While implied volatility is one factor in options pricing, it is not the only factor. A trader must be aware of what other factors are driving an option's price and its volatility.

What Does a Volatility Smile Tell You?

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.

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 with the same underlying asset regardless of the strike price. Yet, in the real-world, this is not the case.

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. The possibility for extreme events needed to be factored into options pricing. Therefore, in the real world, implied volatility increases or decreases as options move more ITM or OTM.

Also, the volatility smile's existence shows that OTM and ITM options tend to be more in demand than ATM options. Demand drives prices which affects implied volatility. 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.

Example of How to Use the Volatility Smile

Volatility Smile
Image by Julie Bang © Investopedia 2019

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

For a rough estimate of whether an option has a u-shape, pull up an options chain that lists the implied volatility of the various strike prices. If the option has a u-shape, options that are ITM and OTM by an equal amount should have roughly the same implied volatility. The further ITM or OTM the greater the implied volatility, with the lowest implied volatilities near the ATM options. If this is not the case, the option does not align with a volatility smile.

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 may take on some form of a u-shape.

This can be useful if seeking an option that has lower implied volatility. In this case, choose an option near the money. If looking for greater implied volatility, choose an option that is further ITM or OTM. Remember, though, as the underlying moves closer or further away from the strike price this will affect the implied volatility. Therefore, maintaining a portfolio of options with a specific implied volatility will require continual reshuffling.

Not all options align with the volatility smile. Before using the volatility smile to aid in making trading decisions, check to make sure the option's implied volatility actually follows the smile model.

The Difference Between a Volatility Smile and a Volatility Skew/Smirk

While near-term equity options and forex options lean more toward aligning with a volatility smile, index options and Long-term equity options tend to align more with a volatility skew. The skew/smirk shows that implied volatility may be higher for either ITM or OTM options.

Limitations of Using the Volatility Smile

First, it is important to determine if the option being traded actually aligns with a volatility smile. The volatility smile is one model that an option may align with, but implied volatility could align more with a reverse or forward skew/smirk.

Also, due to other market factors, such as supply and demand, the volatility smile (if applicable) may not be a clean u-shape (or smirk). It may have a basic u-shape, but could be choppy with certain options showing more or less implied volatility than would be expected based on the model.

The volatility smile highlights where traders should look if they want more or less implied volatility, yet there are many other factors to consider when making an options trading decision.