Option volatility may be a confusing concept since we're not really talking about the volatility of options per-se. Perhaps you've heard the terms implied volatility or historical volatility and aren't too sure what the differences are. These two concepts and option volatility in general are one of the more confusing aspects of options so I wanted to take a page and focus specifically on this topic.

What is volatility in general? The term volatility is meant to describe the range of price movement of a particular instrument (stock, ETF, futures contract, etc). In subjective terms if we were discussing a stock that is currently priced at $40 but has traded between $20 and $60 over the last year, we'd say that stock was pretty volatile.

What's the point of assessing the volatility of a particular instrument? Usually we are attempting to project what the future price of the instrument might be for a given timeframe. In other words, we might look at the past volatility of a stock to get an idea of where it might be trading a month from now. Perhaps we might also want to determine the overall risk a trade might pose. More volatile instruments can also pose a higher risk of being unpredictable.

Put in terms of probability, if I'm evaluating a trade on the stock I mentioned above, I might be looking for a trade that takes advantage of a move back towards $60. The odds might favor this more than for a similarly priced stock that has never moved more than a few dollars in a given year. However, the odds also favor the stock ending up in the opposite direction in a very dramatic way.

In the options world, there are actually a number of different types of volatility. When we talk about the volatility of an instrument based on past behavior, we are talking about historical volatility. When we are talking about what we might expect an instrument to do in the future, we are talking about forecast volatility. These two categories are based on the instrument itself. There is an additional type of volatility that is used to describe the projected volatility of the instrument based on the pricing of the option. This is called implied volatility. Let me spend just a little more time on these different types of volatility.

When we talk about historical volatility, it's usually in the context of a time period. For example, I might talk about the historical volatility of XYZ stock over the last year or the last few months. Again, the point of determining historical volatility is to get an idea of what the future volatility might be. I'll talk about this more in detail later but historical volatility is usually talked about in terms of a standard deviation - a statistical term that measures the distribution of samples (in this case price) over a given period of time. It's sometime also discussed in terms of a percentage.

Future volatility is just another name for what is often referred to as forecast volatility. As an option trader, I'm trying to forecast what volatility might be in the next month or two because that gives me a rough idea of where the underlying instrument might be. Determining forecast volatility is a difficult task because we have to determine what influence the past will have on the future and we have to figure in any anticipated events like earnings and broad market news that might influence the future.

Implied volatility is the volatility anticipated by the overall market (or market makers) and is reflected not in the movement of the underlying instrument but in the pricing of the option. This is different that what we've seen in both historical and forecast volatility. To help illustrate this key difference consider the dilemma an option market maker is in.

The market maker is obligated to make a market for options regardless of the position the trader on the other side of the trade takes. That means if I buy a put contract, they must sell the put contract and take on some amount of risk. In order to compensate for anticipated risk, the market maker will adjust the extrinsic (or time value) portion of the option price. If they perceive additional risk, the price is inflated. If they perceive risk is reduced, the extrinsic value decreases.

The value of implied volatility isn't advertised or posted. A market maker isn't going around saying "I'm now taking options trades on XYZ stock at 31% implied volatility." Instead, we arrive at implied volatility by using one of the options pricing formulas and solving for volatility. I'll talk more about this later.

So far I've been pretty vague about option volatility and probability. That's because in doing so we start delving into statistical math, which can get pretty deep. If you've already learned as much as you want to know, feel free to move on to the next section.

The usual way volatility is calculated is to gather a set of samples of a given instrument over a period of time. For example, we might evaluate the historical volatility of the SPY over the last year by taking the daily closing price as a sample value. With enough samples, it's likely the prices might be distributed in something like the following. Notice that the distribution is somewhat bell shaped. Keep in mind this is a very simplistic view of distribution. In reality, the distribution would be much less even and clean.

Now, take a moment to consider this. In the above image, assuming the time period measured was a month, what would you expect the likelihood is of the underlying instrument remaining below $107 a month from now? If nothing changes, the odds would favor such an outcome. The more volatile the stock, the wider the distribution as the image below illustrates.

Given the above image and the same measured time period, what would you expect the probability is of the same underlying remaining below $107 in the next month? Without coming up with an exact probability, it stands to reason that the probability is much lower. Why? Because the distribution shows that the price has been there and much higher. Therefore it's more probable that the price could exceed that level again.

Hang on because we're going deeper...

One other key concept to introduce is the concept of standard deviation. In simple terms standard deviation describes the way in which the various price outcomes are distributed around the mean. Statistically, one standard deviation (plus or minus) would represent 68.3% of all prices distributed around the mean.

Let's go back to the distribution above with a mean of $102.51. Let's say that one standard deviation is approximately ±12. That means that 68.3% of the outcomes will fall between $114.43 and $90.58. This idea is important because it's what allows us to be able to estimate a probable range of movement into the future.

The
above chart is a probability analysis of the SPY. If you think about it,
this is very much like the statistical distribution images above but turned
on it's side. The one difference is that the statistical distributions were
historical and the probability chart is attempting to project future price
movement. It essentially suggests
that there is a 68% chance that the SPY will be between $114.89 and $110.40
by July expiration. This is not a guarantee because news can come out
tomorrow that changes everything. Volatility might go to twice it's value and
suddenly the probable range expands significantly.

All of this discussion is leading to this final point. Volatility is a factor of all option pricing models. Without spending a lot of time of the actual formula, consider the factors that go into the calculation of option price. These include time until expiration, price of the underlying, the option strike price, expected volatility, interest rate and dividend paid if any.

Of these factors, some have more influence over the price of the option than others. For now, let's leave out interest rate and dividend. That leaves time until expiration, volatility and the relationship between price of the underlying and the option strike price. Of these four, I want to zero in on time until expiration and volatility.

These two are intertwined. Take a look at the probability analysis chart above. Notice that you go out in time that the possible range of price movement widens. When the volatility increases, time has an even greater impact on the width of price movement.

This comes back to option pricing in the following way. Given that there is a direct relationship between volatility of the underlying and the range of price movement and time, it's not hard to imagine that these would impact the price of an option. The farther out in time you go, the pricier the options get as you go out in time.

Typically, you would use an option pricing model such as the Black-Scholes model to calculate the theoretical price of an option. All of the above factors can be plugged into the Black-Scholes model or any other pricing model to arrive at a theoretical price. In this case, the volatility used for calculation is the forecast volatility. When the actual option price is different from the theoretical price, that's when you plug the actual price into the pricing model and solve for volatility.

In bringing the topic of option volatility to a close, I wanted to point out that the above factors are all represented by the option greeks. I also wanted to point out that while we've talked about each of these factors independently, they all work together.