Term Structure of Volatility

Term structure of volatility—also called monthly skew or horizontal skew—is the relationship among the IVs of options in the same class with the same strike but with different expiration months. IV, again, is often interpreted as
the market’s estimate of future volatility. It is reasonable to assume that the market will expect some months to be more volatile than others. Because of this, different expiration cycles can trade at different IVs.

For example, if a company involved in a major product-liability lawsuit is expecting a verdict on the case to be announced in two months, the one-month IV may be low,as the stock is not expected to move much until the suit is resolved. The twomonth volatility may be much higher, however, reflecting the expectations of a big move in the stock up or down, depending on the outcome.

The term structure of volatility also varies with the normal ebb and flow of volatility within the business cycle. In periods of declining volatility, it is common for the month with the least amount of time until expiration, also known as the frontmonth, to trade at a lower volatility than the backmonths,or months with more time until expiration. Conversely, when volatility is rising, the front month tends to have a higher IV than the back months.Exhibit 3.3 shows historical option prices and their corresponding IVs for 32.5-strike calls on General Motors (GM) during a period of low volatility.

In this example, no major news is expected to be released on GM, and overall market volatility is relatively low. The February 32.5 call has the lowest IV, at 32 percent. Each consecutive month has a higher IV than the previous month. A graduated increasing or decreasing IV for each consecutive expiration cycle is typical of the term structure of volatility.Under normal circumstances, the front month is the most sensitive to changes in IV.

First, front-month options are typically the most actively traded. There is more buying and selling pressure.Their IV is subject to more activity. Second, vegas are smaller for options with fewer days until expiration. This means that for the same monetary change in an option’s value, the IV needs to move more for short-term options.Exhibit 3.4 shows the same GM options and their corresponding vegas.If the value of the September 32.5 calls increases by $0.10, IV must rise by 1 percentage point.

If the February 32.5 calls increase by $0.10, IV must rise 3 percentage points. As expiration approaches, the vega gets even smaller.With seven days until expiration, the vega would be about 0.014. This means IV would have to change about 7 points to change the call value $0.10.Vertical Skew The second type of skew found in option IV is vertical skew, or strike skew.Vertical skew is the disparity in IV among the strike prices within the same month for an option class. The options on most stocks and indexes experience vertical skew.

As a general rule, the IV of downside options—calls and puts with strike prices lower than the at-the-money (ATM) strike—trade at higher IVs than the ATMIV. The IV of upside options—calls and puts with strike prices higher than the ATM strike—typically trade at lower IVs than the ATM IV.The downside is often simply referred to as puts and the upside as calls.The rationale for this lingo is that OTM options (puts on the downside and calls on the upside) are usually more actively traded than the ITM options.

By put-call parity, a put can be synthetically created from a call, and a call can be synthetically created from a put simply by adding the appropriate long or short stock position.Exhibit 3.5 shows the vertical skew for 86-day options on Citigroup Inc.(C) on a typical day, with IVs rounded to the nearest tenth.Notice the IV of the puts (downside options) is higher than that of the calls (upside options), with the 31 strike’s volatility more than 10 points higher than that of the 38 strike.

Also, the difference in IV per unit change in the strike price is higher for the downside options than it is for the upside ones. The difference between the IV of the 31 strike is 2 full points higher than the 32 strike, which is 1.8 points higher than the 33 strike. But the 36 strike’s IV is only 1.1 points higher than the 37 strike, which is also just 1.1 points higher than the 38 strike.This incremental difference in the IV per strike is often referred to as the slope.

The puts of most underlyings tend to have a greater slope to their skew than the calls. Many models allow values to be entered for the upside slope and the downside slope that mathematically increase or decrease IVs of each strike incrementally. Some traders believe the slope should be a straight line, while others believe it should be an exponentially sloped line. If the IVs were graphed, the shape of the skew would vary among asset classes.