What Is a Volatility Smile?

A volatility smile refers to patterns and graphs that form by plotting the implied volatility and strike price for an option group with an expiration date and underlying asset. The reason behind naming it a volatility smile is its resemblance to a smiling mouth. When an option's underlying asset is further out-of-the-money (OTM) or in-the-money (ITM) than it is at-the-money (ATM), implied volatility increases. Not all options fall under the scope of the volatility smile.

Fundamentals of Volatility Smile

Volatility smiles result from changes in implied volatility due to the movement of underlying assets more towards ITM or OTM. It would further lead to greater implied volatility. For ATM options, implied volatility would be the lowest.

Although the Black-Scholes model is the primary method for measurement of price options and other derivatives, it doesn't predict the volatility smile. Instead, this model predicts a flat implied volatility curve against varying strike prices. Moreover, it forecasts the same implied volatility for all options with the same underlying assets expiring on the same date. However, the reality is different.

Following the 1987 stock market crash, volatility smiles began to appear in option pricing. They weren't previously present in American markets, indicating a market structure more consistent with what the Black-Scholes model predicts. Following 1987, traders understood that severe outcomes could appear and that markets have a substantial skew. The pricing of options required to consider the potential for dramatic events. That's why implied volatility rises or falls with an increase in OTM or ITM. [1]

Moreover, a volatility smile indicates a higher demand for OTM and ITM than ATM. The erratic Prices are driven by demand, which impacts implied volatility. The aforementioned factor may partially cause this. Extreme incidents can result in significant price changes in options. Implied volatility takes into account the potential for substantial shifts.

How to Use the Volatility Smile?

When comparing options with the same underlying asset and expiration date but different strike prices, volatility smiles can be observed. There can be a U-shape if the implied volatility is shown for the various strike prices. However, the U-shape sometimes has a different shape than seen in the graph below.

Consider an options chain that consists of implied volatility with different strike prices. A U-shaped option indicates that options with the same OTM and ITM have the same implied volatility. More OTM or ITM represents the higher implied volatility. On the other hand, ATM options represent the lowest implied volatilities.

It was also possible to plot the implied volatility of a single option over time and the underlying asset's value. The implied volatility may resemble a U shape as the price moves in or out of the money.

This may be helpful if you're looking for an option with reduced implied volatility. You could potentially pick an option near the money in this scenario. Select a further ITM or OTM option if you want more implied volatility. But remember that the implied volatility will change when the underlying asset moves closer to or further away from the strike price. As a result, regular realignment is essential to maintain a portfolio of options with certain implied volatility.

Alignment of all options with volatility smile is optional. Verify that the option's implied volatility genuinely adheres to the smile model before employing the volatility smile for trading decisions.

Limitations of Using the Volatility Smile

Finding out whether the option being traded genuinely corresponds with a volatility smile is crucial. One model that aligns with the option is the volatility smile. However, the model that aligns more with the forward or reverse skew/smirk is implied volatility.

Additionally, the volatility smile (if applicable) may have a vague U-shape due to other market factors like supply and demand (or smirk). It could have a basic and choppy U-shape, with certain options exhibiting more or less implied volatility than the model's prediction,

The volatility smile indicates all the options for traders to get more or less implied volatility. However, many other factors affect the options trading decision-making process.

[1]https://pages.stern.nyu.edu/~dbackus/GE_asset_pricing/BCDG%2087%20crash%20Jan%2010.PDF