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What is the relationship between implied volatility and the volatility skew?

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posted Jul 14 by Chetan Hindu

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The volatility skew refers to the shape of implied volatilities for options graphed across the range of strike prices for options with the same expiration date. The resulting shape often shows a skew or smile where the implied volatility values for options further out of the money are higher than for those at the strike price closer to the price of the underlying instrument.

Implied Volatility
Implied volatility is the estimated volatility of an asset underlying an option. It is derived from an option’s price, and is one of the inputs of many option pricing models such as the Black-Scholes method. However, implied volatility cannot be directly observed. Rather, it is the one element of the options pricing model that must be backed out of the formula. Higher implied volatilities result in higher option prices.

Implied volatility essentially shows the market's belief as to the future volatility of the underlying contract, both up and down. It does not provide a prediction of direction. However, implied volatility values go up as the price of the underlying asset goes down. Bearish markets are believed to entail greater risk than upward trending ones.

Traders generally want to sell high volatility while buying cheap volatility. Certain option strategies are pure volatility plays and seek to profit on changes in volatility as opposed to the direction of an asset. In fact, there are even financial contracts which track implied volatility. The Volatility Index (VIX) is a futures contract on the Chicago Board of Options Exchange (CBOE) that shows expectations for the 30-day volatility. The VIX is calculated using the implied volatility values of options on the S&P 500 index. It is often referred to as the fear index. VIX goes up during downturns in the market and represents higher volatility in the marketplace.

Types of Skews
There are different types of volatility skews. The two most common types of skews are forward and reverse skews.

For options with reverse skews, the implied volatility is higher on lower option strikes than on higher option strikes. This type of skew is often present on index options, such as those on the S&P 500 index. The main reason for this skew is that the market prices in the possibility of a large price decline in the market, even if it is a remote possibility. This might not be otherwise priced into the options further out of the money.

For options with a forward skew, implied volatility values go up at higher points along the strike price chain. At lower option strikes, the implied volatility is lower, while it is higher at higher strike prices. This is often common for commodity markets where there is a greater likelihood of a large price increase due to some type of decrease in supply. For example, the supply of certain commodities can be dramatically impacted by weather issues. Adverse weather conditions can cause rapid increases in prices. The market prices this possibility in, which is reflected in the implied volatility levels.

answer Jul 15 by Sherlyn Mishra
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