Before I begin this lesson I must inform you that I’ve got both good news and bad news for you, the retail trader/investor, who is attempting to learn about volatility. So which would you like first, the good news or the bad news? I always like to begin with the bad news: The bad news is that volatility is one of the most crucial yet frequently misunderstood concepts in the options trading game. Moreover ( for the less quantitatively inclined among you), it is one of the most purely mathematical, deriving straight from probability theory. The terms “standard deviation,” “mean reversion” and “serial correlation” are each important for an overall understanding of volatility.

What about the good news, you say? Well the good news is that for the retail trader and small investor, mastering the complexities of volatility is a nicety rather than a necessity. You simply don’t have to learn all the same nuances of volatility that the professional trader must. For the retail trader, various other factors play a much greater role in your trading success -- chief among these being the establishment of your individual threshold for risk; the adroit selection of stocks; and the timing of price movements and trends. Nonetheless, every options trader should have a grasp at least of a few fundamental principals of volatility, and the outlining of these is my task at hand.

Let’s cut to the chase. First and foremost, volatility is an essential concept in determining the value of an option. It can be looked at from two angles: conceptually and mathematically. Conceptually, Volatility is essentially the measurement of a stock’s ( or other underlying’s) tendency to move up and down in price over a given period of time. It is also, as we shall see, the only variable in an option pricing model not known with certainty in advance. Mathematically, volatility can be defined as is the annualized standard deviation of daily returns of a given underlying. Note that options practitioners always talk about volatility in terms of percentages. For example, a rise in “vol.” in stock (or Index) ABC from 100-101 is equal to a rise in stock (or Index) BCD from 300-303, because in both cases the changes is equal to 1 percent.

It is important to know that volatility has a straightforward relationship with the option’s price: As the percentage of volatility increases, the price of the option likewise increases. Why is this so? Follow the logic: First, an options volatility is tied to the price movement of the underlying instrument. Second, a higher volatility means that the stock has a greater likelihood of movement. Third, a stock with a greater likelihood of movement has a higher probability of reaching the exercise price. And fourth, a stock with a higher probability of reaching its exercise price will have a relatively higher price than one with a lower probability of reaching the exercise price. Mathematically, all this can be demonstrated mathematically, and graphically by a look at low medium and high volatility distribution curves. But you don’t need to get into all of that!

But, you might ask, what about the difference between puts and calls? Does volatility affect each differently, such that higher volatility might increase the value of a call while decreasing the value of a put, or vice versa? This might make intuitive sense, but the answer is no. It is a statistical fact that volatility is “nondirectional.” This means that if the market is expecting a higher volatility, it is expecting movement per se. This movement can be either up or down. Thus when a higher volatility is assigne, the prices of both calls and puts rise.

If we examine a chart of the history of a stock’s price movement, we would discover that each individual stock passes through periods of low volatility and also periods of high volatility. What accounts for these fluctuations in price? There are numerous possibilities. Macro and or microeconomic factors affecting the particular company could certainly do it. Also, macroeconomic influences on the company’s sector or industry could also be a cause. Maybe the investors of the particular stock heard a rumor-- who knows? The point is the causes for a stocks price fluctuation are myriad.

I lied. I am going to through a little bit of math at you, and here it is. Regardless of the cause, volatility tends to be mean-reverting.This is a hugely important fact for volatility traders, those guys who buy and sell chiefly by looking at a stock’s vol. levels. Over the short and intermediate terms, when markets become imbalanced, volatility fluctuations can be violent. But when the underlying market finally achieves balance, volatility will always revert back to its long-term mean.

Volatility over a given time period is highly correlated to the volatility of the previous identical time period. In other words, the volatility of the next 30 days is statistically likely to be similar o the last 30 days. This interesting characteristic is referred to as serial correlation.

Volatility fluctuates inversely with respect to time. As short term volatility is moved away from the mean by various and sundry short term events, it has less chance to return to the mean because of time restriction. Longer-term volatility, on the other hand, has a greater amount of time to revert to that mean.

It is important to note that options practitioners actually describe volatility in four different ways. While these different types of Vol. Are not going to play as big a role in your, the retail trader’s, trading decisions, you must understand what traders are talking about.

Typically, volatility is broken down into 4 types:

1. Historical Volatility. Historical volatility is, for the most part, what we have been talking about so far it this lesson. It is the measure of price changes of an instrument (a stock, index, etc.) over a given period of time. Think of it as the instruments “up and downness,” for a short and cute definition. And, to repeat, we can get fancy and look at it mathematically as the stock’s annualized standard deviation of daily returns. But let’s keep it simple…

2. Expected Volatility is a very subjective creature. This simply refers to the trader’s best guess as to what volatility will be. Of course, these aren’t BLIND guesses, most traders study historical charts and look at market conditions to come up with the expected volatility value. But they are estimates nonetheless.

3. Future Volatility is, I like to think, kind of the mathematician’s way of saying Expected volatility. By definition it is the Annualized standard deviation of daily returns during a yet to be specified future period of time. This period typically extends from the present to the option’s expiration. But hold on a minute: for a future period of time? How can a trader now this value? Well, he can’t; only historical volatility can be known with certainty, because it has already happened!

Traders use sophisticated pricing models to determine the theoretical value of an option. Most of these pricing formulae derive in some way from the Black-Scholes model. Now these models have a number of variables that must be input in order for them to spit out the theoretical value. These variables include Exercise price, Underlying price, Time to Expiration, Interest Rates, Dividends, and Volatility. The model plugs all these numbers into a model developed by a rocket scientist and pops out a theoretical value. Now look hard: which of the above input-values is not known ahead of time, and with certainty? You guessed it : VOLATILITY. So the volatility values that these sophisticated models use to produce their vaunted theoretical values are really no more than estimates! This may come as a shock to some of you that guesswork plays such a role in pricing models, but it does. To summarize, Future Volatility is the number needed to plug into an option pricing model in order to determine an option’s theoretical value.

4. Implied Volatility. I saved the hardest one for last! Implied Volatility is the volatility value ( remember, expressed in % form) that justifies or implies the current market price of the option. To understand what the heck this means, let’s go back to our discussion of the pricing model above. Recall we said that the trader plugs in various values into his sophisticated pricing model or formula, including one for Volatility ( the “future Vol. Number”), and out pops a number called the theoretical value of an option.

OK, so for example, we plug these values in the model to obtain the theoretical value of the July ABC 55 Call, and we come up with a value of $5 ¼. But wait, when we look at our monitor, we see that the actual market price ( what the option is actually trading at), is only $5 even.

Using a little high school algebra, we do the following. We simply replace the theoretical value we just obtained with the actual market price of the option, and run the pricing model in reverse. We are thus effectively solving for the Volatility value that would be needed to yield up a theoretical value that equals the actual market value of the option. The number we come up with ( in % form) is the Implied Volatility value. Again, this value tells us the volatility that the market is implying for the underlying via its pricing of the specific option.

I told you it was a little complicated. But really Implied value is one of those features of volatility that professional traders need to know more than the retail trader. In a nutshell, the professional trader determines whether an option is “overvalued”, “undervalued” or at “fair value” by comparing the Implied volatility value with the Future volatility value. For the professional trader, if the Future Vol. is higher than the implied vol, then the option is said to be undervalued. If the Future vol. is lower than the implied vol, then the option is said to be overvalued. And if the Future. vol. is exactly equal to the Implied vol, then the option is said to be at Fair Value.

Note: This does NOT mean that an option’s trader merely buys the undervalued options and sells the overvalued ones like a monkey. Much more goes into it than that. But then that is the subject of a future lesson…

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