Option Volatility: Vertical Skews and Horizontal Skews
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.
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.