Estimating Volatility
As I have pointed out several times in these commentaries, the volatility that counts in determining the current value of an option, put or call, is the future volatility between now and expiration of the option. The future values of the underlying are unknown today, and hence the future volatility is also unknown. So to arrive at a volatility that is useful to you as an options trader, you have to predict the future–an ominous task.
One natural approach to predicting the future is to assume that the future is going to be like the past. In many cases, this approach is valid; in many cases, it is not. For example, most people know you cannot conclude that a stock price will climb in the next six months just because it has been going up for the last six months.
However, it just happens that volatility behavior of a stock tends to persist into the future, and the natural approach to predicting the future of volatility is not at all invalid. A part of the reason for this is that volatility is not as visible a quantity as the rise or fall of a price. Another part of the reason is that volatility represents uncertainty about the true value of a company, and this uncertainty is in a sense a characteristic of the company and its structure, which do not change much across time.
The usual way to estimate future volatility is to choose a look-back period, such as the 100 days we use on this site, and measure the volatility over this recent historical period by computing the standard deviation of the percentage change from each day in the period to the next. This gives you the one-day volatility over the last 100 days, and your assumption is that this one-day volatility will continue over the next time period.
Once you have the one-day volatility, you can use the square root law to compute the volatility over any period, as explained in previous commentaries. So, for instance, the volatility over 16 days is four times the one-day volatility. And if you are looking at an option with 16 days left to expiration, you would estimate the volatility over the next 16 days as four times the one-day volatility you have computed.
Of course, your estimate relies on the look-back period, in our case 100 days. If you had chosen 50 days, or 20 days, you would naturally have gotten a different answer–close, but different. One thing you might do to persuade yourself that you have a valid number is make this computation for different look-back periods. Here are the one-day values you get when you compute the volatility of IBM over the following look-back periods:
| Look-back | One-day volatility |
|---|---|
| 100 | 2.53% |
| 80 | 2.16% |
| 60 | 2.05% |
| 50 | 2.00% |
| 40 | 2.07% |
| 20 | 2.42% |
| 10 | 2.63% |
So looking back 100 days from today, August 18, we find that IBM has fluctuated typically about 2.53% per day; looking back only 50 days, we find a typical fluctuation of only 2.00% per day; and looking back only 10 days we find a typical fluctuation of 2.63% per day. And the other look-back periods are likewise different from these and from one another. Which one should you use?
This is an important question, because your opinion of the value of an IBM option depends on the volatility you use, and as we saw in the previous two commentaries, this value is not robust relative to the volatility. Small changes in the volatility can lead to large changes in the option value.
There are a number of reasonable ways to look at this problem, and I will discuss them in upcoming commentaries.