Understanding the difference between Option Volatility Smile & Skew

What is the Volatility Smile
The volatility smile is a graphical representation of the implied volatility of options with the same expiration date but different strike prices. It describes the pattern that arises when plotting the implied volatility of options against their respective strike prices on a graph. Typically, implied volatility is assumed to be constant across all strike prices and maturities in the Black-Scholes model. However, in practice, this is not always the case, and the volatility "smile" or "smirk" arises as a graphical representation of differences in implied volatility across strike prices. The volatility smile can take on different shapes depending on the underlying asset and market conditions, but it generally slopes upwards on both ends, forming a "smile" shape. This indicates that options with strike prices that are further from the current market price tend to have higher implied volatility. (Deep Out of the money - OTM options). Commonly, this IV at the wings accounts for "tail risk", where external shocks can create outsized moves on an asset. Traders noticed after the market crash of 1987 that market participants were willing to pay more for option protection that were deep out of the money; and also reflects the market implied possibility of large movements in the underlying asset.

BTC Implied Option Volatility Smile Using Transactional Data 5/3/23

Volatility Smile vs Volatility Skew
Volatility skew refers to the difference in implied volatility between out-of-the-money (OTM) options and at-the-money (ATM) options, for a specific expiration date. It is a measure of how the market perceives the potential risks and rewards of different option in differing maturities and strikes. Volatility skew and volatility smile are related concepts, as they both inform an aspect of the shape of the implied volatility curve across different strike prices. The volatility smile typically refers to the shape of the implied volatility curve for options (all strikes) with the same expiration date, while the volatility skew is specifically concerned with the difference in implied volatility between OTM and ATM options. When there is a steep volatility skew, the implied volatility of OTM options is higher than that of ATM options, indicating that the market perceives a higher likelihood of large price movements in the underlying asset. This can occur in markets that are experiencing high levels of uncertainty or where there is a heightened risk of sudden price changes. It can also take place in the lead up to large news releases at a macro level, like the FOMC statement; or at a more micro (specific) level like an earnings release. The volatility smile, on the other hand, describes the overall shape of the implied volatility curve across different strike prices. It can be used to gain insights into market expectations for future price movements and assess the potential risks and rewards associated with different options.

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