Level: Intermediate

Introduction

Volatility Skew is a broad term that refers to the distribution of implied volatilities (IV) across strike prices for a single expiration. It could also refer to an IV-Expiry graph, but we will be focusing on the more common definition. For a two-dimensional graph, the values plotted for a skew would be the strike price on the x-axis, and the implied volatility of that strike on the y-axis.

Keep in mind, though, that in financial lingo, volatility skew and volatility smile are two separate terms, both of which describe the shape of the graph.

Volatility skew graphs are commonly available in most trading platforms.. However, to graph multiple expirations, you would need a volatility surface, which graphs expiration on the z-axis. These charts are not commonly available, but you can view an example below.

Volatility Smile

A volatility smile is a pattern in which the Strike-IV graph looks like the following:

This means that the ATM call is priced lower than the OTM options, both calls and puts. The actual price, of course, would be larger or smaller depending on the type, but the relative price difference is calculated from the discrepancy from a number given from an options pricing model (ex. Black-Scholes).

The discrepancy could be caused by a variety of factors, which depend on the type of security being analyzed. For example, a smile would represent fear of either a move to the upside or to the downside because it shows that people are willing to pay more than expected for the options, which are often used as insurance.

Volatility smile is more common in options with close expiries in the stock market or in the foreign exchange market in general.

Volatility Skew

Volatility skew is a situation in which strikes for only one side of strike prices have a higher implied volatility.

 

Some people call the reverse skew a “smirk,” and there are other names for different graphs. When someone refers to “skew,” they are most probably referring to reverse skew.

Reverse skew is also the most common scenario for longer-dated expiries in the equity market. This is because lower strike puts are purchased to shield against market drops. However, in other markets, like the futures market, a forward skew might exist to protect against a price spike (ex. utilities).

Evolution of the IV Surface

So far, we have been looking at what the numbers themselves actually represent. Let’s take a look at the derivative of these graphs, otherwise known as the evolution.

“Sticky strikes” is a term to represent a situation where if the spot price changes, the IV surface is unaffected for a certain strike. This is also called stick-to-strike or sticky-by-strike.

“Sticky moneyness” or sticky delta or just moneyness is a situation where if the spot price changes, the IV surface is unaffected for a certain delta. Delta is simply the variation in an options price relative to the stock price.

Modeling Methods

There are two ways that the IV can be modeled in the case of a volatility smile.

• Stochastic Volatility – Quite advanced, but it simply uses a random Brownian motion process to influence a stochastic model, which cannot be exactly predicted, but can be analyzed.
• Local Volatility – Simply the general definition of IV, where it is the function of an options-pricing model.

Conclusion

The volatility skew is a tool that lets one see how investors are pricing options, not just in raw dollar terms, but compared to the Black-Scholes model. There are many terms to represent the shape of the curve, and the change in the IV Surface has its own terminology.