« Primer on Options Volatility »

Volatility refers to the tendency of an underlying to fluctuate in price.

Nearly all underlying assets, be they stocks, bonds, futures, et al, change in value over time. The only difference is that certain underlying assets tend to fluctuate in price more than others. The tendency of a particular underlying to move in a highly or lowly volatile manner brings about a corresponding effect on the potential expiration value of options on that underlying, and thus is a significant contributor to the time value premia of those options.

Depiction of low volatility versus high volatility in price action of a security

Simplistically, volatility is a measure of risk. In this context, risk refers to the probability of the option’s finishing in-the-money, at-the-money or out-of-the-money [see definition of "moneyness" of an option]. Intuitively, it can be understood that the higher the volatility in the underlying asset, the wider the potential range that the underlying can trade within, at or before expiration.

This particular element of uncertainty, namely volatility, has a huge effect on the price of options. Options on underlying assets with a high level of volatility are more expensive than options on underlying assets with a low level of volatility (all other variables held constant). This is because of the fact that writers (sellers) of options feel it necessary to demand a higher level of time value premium on those options in order to counter the wider range of potential expiration values. 

The kind of options - calls or puts - does not matter when it comes to the expensiveness of options on a highly volatilite underlying asset. Since the asset can make a large up-move or a large down-move, there is a higher level of risk in selling any kind of options on the underlying; hence both calls and puts trade at a higher price than do otherwise comparable options.

Mathematically, volatility is usually defined as the annualized standard deviation of a stock’s daily price fluctuations. As such, it (volatility) is often stated as a percentage when used as an input in options pricing models.

Take a look at the following chart, which helps illustrate how volatility levels differ from one underlying asset to another, and also from period to period on a given underlying asset itself... 

Chart showing trading action and Bollinger Band Width (black line) of WMT and OXY, over an 8-month period in 2006

The volatility of one underlying asset is usually independent of that of another underlying asset. Moreover, the volatility level is not always constant for a given underlying asset; it often varies depending upon market conditions and upon the other technical forces that are at play on the underlying.

The chart, above, gives us an excellent illustration, firstly, of how two stocks that started and ended a given period at virtually the same price actually traded within different ranges in the interim and, secondly, of how the volatility of each stock changed over the given period. The trends in volatility of each underlying can be seen in its respective Bollinger Band Width in the chart above (bollinger band width is a measure of volatility and is derived from a running measure of the standard deviation of the underlying).

Each stock started the chosen period at 47.5 and even closed the period at exactly that price. You'll also notice that even though the paths that they traversed were quite different, their respective price ranges were relatively similar. The stock (WMT) in the upper pane traded between 42.5 and 52.0, while the one (OXY) in the lower pane traded between 44.0 and 55.0. Thus, the range of the first stock was 9.5 and that of the second stock 11.0. There is a difference, but it's not drastic.

When we look closely at the volatility levels of each of the stocks, however, we notice vastly different readings in Bollinger Band Width of each of the stocks [note that the bollinger band width scale is depicted on the left hand side of the charts]. OXY (on the bottom pane) which showed Bollinger Band Width as high as 12 and as low as 3, was clearly more volatile than its counterpart, WMT, which showed Band Width between 7 and 1.5.

Given this information, we would expect to find that the options on OXY trade at a higher price than those on WMT. And this actually was the case. We'll save you the experience of having to delve into the option price tables; after all, you certainly understand the concept intuitively. But what we would like to do is to very fleetingly introduce the concept of implied volatility, at this point.

As it turns out, options gurus have discovered a nifty measure of time value premium, and they have aptly called it "implied volatility." Implied volatility numbers are often used as an input in (or derived from) options pricing formulae. But, as we said earlier, we'll leave an in-depth discussion of implied volatility for another time. For now, we'll show you a couple of implied volatility charts and briefly describe what is seen on the same...

The following graphs depict the trends in implied volatility (and actual historical volatility) of WMT and OXY options, respectively, over the 12 months ending November 2006.

Chart depicting Implied Volatility of WMT options between Dec ’05 and Nov ‘06

Chart depicting Implied Volatility of OXY options between Dec ’05 and Nov ‘06

What the two charts show us is that options on OXY typically trade at a much higher level of implied volatility (24%-41%) than do options on WMT (13%-25%). In other words, all other variables held constant, options on the more volatile OXY, trade with a higher time value premium (and thereby cost more) than do options on the less volatile WMT.