By John Summa, CTA, PhD, Founder of OptionsNerd.com

One of the most interesting aspects of volatility analysis is the phenomenon known as a price skew. When options prices are used to compute implied volatility (IV), what becomes apparent from a look at all the individual option strikes and associated IV levels is that the IV levels for each strike are not always the same - and that there are patterns to this IV variability.


While you may have seen IV values for a particular stock before, these usually are derived from an average (sometimes weighted) of all strikes, or near the money strikes, or even at-the-money strikes of the nearest trading month. As you take a closer look, however, which we will do here, the variability of IV along the option strike chain will reveal what is known as an IV skew.


There are two main groups of skews - horizontal and vertical. The vertical skew will be looked at first. In this case, you'll see how volatility changes depending on the strike price. Then we'll check out an example of a horizontal skew, which is a skew across time (options with different expiration dates).

Forward and Reverse Skews
There are two main types of vertical IV skews - forward (positive) or reverse (negative). The options on stock market indexes (i.e., OEX, SPX) have a permanent reverse IV skew. This pattern of IV variability is common to most equity market indexes and many of the stocks that make up those indexes.

With a reverse vertical IV skew, at lower option strikes IV is higher and at higher option strikes IV is lower. Figure 12 presents an example of a reverse IV skew on the S&P 500 stock index call options.

Generated using OptionVue 5 Options Analysis Software.
Figure 12: Reverse IV skew on S&P 500 index call options. IV falls moving from lower to higher points on the strike price chain, as seen in the IV levels highlighted in yellow.

The first of three data columns (next to the strikes) in Figure 12 contain option market prices and the far right column contains time premium on the options. The arrows point to the higher and lower strikes in both expiration months with associated IV levels, which indicates vertical reverse skews.

It is easy to identify the vertical reverse skew in Figure 12. For example, the August 1440 call option has an IV of 28.21% compared with a lower IV on the higher August 1540 call strike, which has an IV of 23.6%. The lower the options on the strike chain (whether calls or puts), the higher the IV will be.

September options are included in Figure 12 and the skew is present there, too. Note that the IV levels across time (August vs. September) are not the same on these strikes. Instead, the front month August options have developed a higher level of IV. This is known as a horizontal skew, which is discussed below.

As you can see in Figure 13, which contains implied volatility levels on S&P 500 stock index put options (for the same day as in Figure 12), the IV on August 1460 put strike is 26.9%. As you move down the strike chain, however, IV rises to 37.6%, as seen on the 1340 put strike. These IV levels were captured at the close of trading following a big drop in the S&P (-44 points) on August 9, 2007. While the skew is always there, it can intensify following market drops. The reverse forward skew exists largely in response to the possibility of a market crash that may not be captured in the standard pricing models. That is, risk is priced into the options to take into account the possibility, however remote at any point in time, of a large market decline.

Generated using OptionVue 5 Options Analysis Software
Figure 13: Reverse IV skew on S&P 500 index put options. IV falls moving from lower to higher points on the strike price chain, as seen in the IV levels highlighted in yellow.


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Figure 14: Forward (Positive) IV skew on March Coffee call options. IV levels rise at higher points on the strike price chain.

Figure 14 presents a vertical forward skew on March coffee options. With a forward vertical IV skew, at lower option strikes IV is lower and at higher option strikes IV is higher.





With commodities, the higher IV typically rises on higher strikes due to the perceived risk of a price explosion to the upside resulting from a sudden supply disruption. The IV levels might increase on out-of-the-money calls, for example, if there is growing possibility of a frost that could disrupt supply. If the event does not transpire, IV levels might quickly return to more normal levels.


The skews identified in Figures 12 through 14 might be best characterized as "smirks", but it is possible to find different patterns of variability. Patterns may at times resemble a "smile", which means that the IV levels on out-of-the-money puts and calls are elevated relative to the near or at-the-money options. This might arise ahead of corporate news announcements or pending news of a nature that will likely result in a big move for a stock. The reverse skew of Figures 12 and 13, on the other hand, is always present, although the relative and absolute levels of the IV on the strikes may change depending on levels of investor fear in the market at any one time.

Horizontal Skews
In Figure 15, a horizontal skew can be seen on March coffee call options. There is a 5% difference between IV levels on the Dec 155 call options and March 155 call options, with the front month having higher levels. Generally speaking, it is possible for options in any one month to acquire higher IV levels than other months, and as with commodities, it is true for stocks. This phenomenon is largely driven by expected price moves surrounding an impending news event or possibly weather or supply conditions that may impact the price of commodities. These skews can arise and disappear as the news event approaches and then passes.

Generated using OptionVue 5 Options Analysis Software
Figure 15: Horizontal IV skew on March coffee call options. IV for December out-of-the-money call options has a forward positive skew. The options are also trading at higher IV levels than their counterparts in March (i.e., 155 call options).


Conclusion
In this segment of the volatility tutorial, several types of option IV skews are presented. The reverse skew, forward skew and horizontal skew. These are common types of skews that are found in option markets. The exact shape may vary in each real world case but the basic structures will repeat again and again. Strategies can be applied to identify skews that optimize the IV pricing and possible changes in skew pricing that can occur when a skew returns to pre-skew levels.


Next: Option Volatility: Predicting Big Price Moves »

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