# Volatility Smile and Surfaces: Definition and Importance

Volatility Smile is a graph that shows the implied volatility of options at different strike prices for a single expiration date. The smile is so named because it resembles a smiling mouth. Read more.

## What Is A Volatility Smile?

A Volatility Smile is a graphical representation that emerges when we plot the strike price and implied volatility of a set of options that share the same underlying asset and expiration date. This graph typically takes on a U-shaped pattern, hence the name “Volatility Smile”. The implied volatility tends to increase when the underlying asset of an option is either significantly in the money (ITM) or out of the money (OTM), compared to being at the money (ATM). However, it’s important to note that not all options exhibit Volatility Smiles.

## How to Use the Volatility Smile (with an example)

The Volatility Smile is a concept used in options trading that describes a pattern where at-the-money options tend to have lower implied volatilities than in- or out-of-the-money options. The graph of these volatilities forms a curve that is shaped like a smile, hence the name.

Let’s illustrate this with an example:

Suppose we have a stock, XYZ, currently trading at ₹50. We are looking at options with the same expiration date but different strike prices.

1. At-the-money (ATM) option: This is an option where the strike price is the same as the current trading price of the underlying asset. In our case, an ATM option would have a strike price of ₹50. Let’s say the implied volatility of this option is 20%.
2. In-the-money (ITM) option: This is an option that would be profitable if it were exercised immediately. For a call option, this means the strike price is below the current trading price of the underlying asset. For a put option, the strike price is above the current trading price. In our case, an ITM call option might have a strike price of ₹45, and an ITM put option might have a strike price of ₹55. Let’s say the implied volatilities of these options are 25%.
3. Out-of-the-money (OTM) option: This is an option that would not be profitable if it were exercised immediately. For a call option, this means the strike price is above the current trading price of the underlying asset. For a put option, the strike price is below the current trading price. In our case, an OTM call option might have a strike price of ₹55, and an OTM put option might have a strike price of ₹45. Let’s say the implied volatilities of these options are also 25%.

If we were to plot these implied volatilities against the strike prices, we would see a curve that dips down at the ATM option and rises at the ITM and OTM options, forming a shape that looks like a smile. This is the Volatility Smile.

The Volatility Smile can be used to identify mispriced options and to manage risk. For example, if an option’s implied volatility is significantly higher or lower than what the Volatility Smile would predict, it might be over- or under-priced. Similarly, by understanding how volatility surfaces change with the strike price, traders can better manage their risk exposure.

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

While the Volatility Smile is a common pattern in near-term equity options and forex options, index options and long-term equity options tend to align more with a Volatility Skew or Smirk. This skew/smirk indicates that implied volatility may be higher for ITM or OTM options.

## Importance of The Volatility Smile

The Volatility Smile is a significant concept in the world of finance, particularly in options trading. Its importance is rooted in several key areas:

1. Market sentiment indicator: The Volatility Smile can provide insights into the market’s sentiment towards a particular asset. If the smile is more pronounced, it may indicate that the market expects significant price movement, either upwards or downwards.
2. Risk management: The Volatility Smile helps traders and risk managers understand the risk associated with different strike prices. It can be used to adjust risk management strategies based on the perceived volatility of different options.
3. Pricing of options: The Volatility Smile is crucial in the pricing of options. Traditional models like Black-Scholes assume constant volatility, but in reality, volatility changes with different strike prices. The Volatility Smile helps to account for this discrepancy, leading to more accurate pricing.
4. Identifying arbitrage opportunities: The Volatility Smile can sometimes reveal arbitrage opportunities. If the implied volatility for an option is significantly different from the expected volatility based on the smile, it may present an opportunity for profit.
5. Understanding market anomalies: The existence of the Volatility Smile is considered a market anomaly, as it contradicts the assumptions of constant volatility in traditional financial models. Studying the Volatility Smile can help researchers and practitioners better understand these anomalies and improve financial models.

## Limitations of Using the Volatility Smile

Before using Volatility Smiles as a trading aid, it’s crucial to confirm that the option’s implied volatility actually follows the smile model. Not all options align with the Volatility Smile. Some may align more with a reverse or forward skew/smirk.

Moreover, due to other market factors like supply and demand, the Volatility Smile may not always be a clean U-shape. It could be somewhat choppy, with certain options showing more or less implied volatility than what the model would predict.

Lastly, while the Volatility Smile can guide traders towards options with more or less implied volatility, it’s essential to consider other factors when making trading decisions. The Volatility Smile is just one piece of the puzzle.

## FAQs

### What is a Volatility Smile?

A Volatility Smile is a graphical representation of the implied volatility of a group of options with the same underlying asset and expiration date but different strike prices. The smile is so named because it resembles a smiling mouth, with the implied volatility of out-of-the-money (OTM) and in-the-money (ITM) options being higher than the implied volatility of at-the-money (ATM) options.

### What are the implications of Volatility Smiles for options traders?

Volatility Smiles can have a significant impact on option prices. For example, if the implied volatility of OTM options is higher than the implied volatility of ATM options, then a call option with an OTM strike price will be more expensive than a call option with an ATM strike price. This is because the options trader is paying for the higher expected volatility of the OTM option.

### What is the difference between a Volatility Smile and a volatility surface?

The Volatility Smile refers to a single expiry, whereas the volatility surface refers to a set of maturities. In other words, the Volatility Smile shows the relationship between implied volatility and strike price for a single expiration date, while the volatility surface shows this relationship for multiple expiration dates.

### What are some of the limitations of Volatility Smiles?

Volatility Smiles are not perfect representations of the expected volatility of an underlying asset. This is because they are based on the prices of options, which are influenced by a number of factors other than volatility, such as interest rates and dividends. Additionally, Volatility Smiles can change over time, so they may not be accurate for long-term predictions of volatility.

### How can I use Volatility Smiles to make better trading decisions?

Volatility Smiles can be used to make better trading decisions by providing insights into the market’s expectations of future volatility. For example, if the implied volatility of OTM options is higher than the implied volatility of ATM options, then this may indicate that the market is expecting higher volatility in the future. This information could be used to make decisions about whether to buy or sell options or to choose the strike price of an option.