Volatility skew is a options trading concept that states that option contracts for the same underlying asset—with different strike prices, but which have the same expiration—will have different implied volatility (IV). Skew looks at the difference between the IV for in-the-money, out-of-the-money, and at-the-money options.
Implied volatility can be explained as the uncertainty related to an option's underlying stock, and the changes triggered at different options' trading prices. IV is the prevalent market view of the chance that the underlying asset will reach a given price. In-, at, and out-of-the-money refers to the strike price of an options contract as it relates to the going market price for that asset.
Volatility skew is important to watch if you buy and sell options because the implied volatility rises as the uncertainty around its underlying stock increases.
The Volatility Smile
When options first traded on an exchange, volatility skew was very different. Most of the time, options that were out-of-the-money traded at inflated prices. In other words, the implied volatility for both puts and calls increased as the strike price moved away from the current stock price—leading to a "volatility smile" that can be witnessed when charting the price data.
That is a situation in which out-of-the-money (OTM) options (puts and calls) tended to trade at prices that seemed to be "rich" (too expensive). When the implied volatility was plotted against the strike price, the curve was U-shaped and resembled a smile. However, after the stock market crash in October 1987, something unusual happened to option prices.
There is no need to conduct extensive research to understand the reason for this phenomenon. OTM options were usually inexpensive—in terms of dollars per contract. They were more attractive for speculators to buy than as something for risk-takers to sell—the reward for selling was small because the options often expired worthlessly.
Because there were fewer sellers than buyers for both OTM puts and calls, they traded at higher than "normal" prices—as is true in all aspects of trading (i.e., supply and demand).
The Effects of "Black Monday"
Ever since Black Monday (Oct 19, 1987), OTM put options have been much more attractive to buyers because of the possibility of a gigantic payoff. In addition, these puts became attractive as portfolio insurance against the next market debacle. The increased demand for puts appears to be permanent and still results in higher prices (i.e., higher implied volatility). As a result, the "volatility smile" has been replaced with the "volatility skew". This remains true, even as the market climbs to all-time highs.
In more modern times, after OTM calls became far less attractive to own, but OTM put options found universal respect as portfolio insurance, the old volatility smile is seldom seen in the world of stock and index options. In its place is a graph that illustrates increasing demand, as measured by an increase in implied volatility (IV) for OTM puts along with a decreased demand for OTM calls.
That plot of strike vs. IV illustrates a volatility skew. The term "volatility skew" refers to the fact that implied volatility is noticeably higher for OTM options with strike prices below the underlying asset's price. And IV is noticeably lower for OTM options that are struck above the underlying asset price.
IV is the same for a paired put and call. When the strike price and expiration are identical, then the call and put options share a common IV. This may not be obvious when looking at options prices.
There currently exists a number of investors (and money managers) who never again want to encounter a bear market while unprotected, i.e., without owning some put options. That results in continued demand for puts.
The following relationship exists: IV rises when markets decline; IV falls when markets rally. This is because the idea of a falling market tends to (often, but not always) encourage (frighten?) people to buy puts—or at least stop selling them. Whether it is increased demand (more buyers) or increased scarcity (fewer sellers), the result is the same: higher prices for put options.