# Option Probabilities: The Volatility Cone

March 27th, 2015
in contributors

Online Investing Academy Article of the Week

In the last three articles in this series, Part 1, Part 2 and Part 3, I've been discussing probabilities as applied to option trading. Last time I mentioned there are software tools that do the heavy lifting of these calculations for us. Below is an example of one of these, the Volatility Cone.

First, look at this price chart for GLD, the exchange-traded fund that tracks the price of gold. As of March 13 that chart looked like this:

The current price was in a demand zone in the \$110-113 area. This zone had originated in early 2010, not shown on the chart. There was a supply zone overhead in the \$123-125 area.

In this example I'm ignoring the nearby supply area around \$116, which of course we couldn't do in real life. The point here is to illustrate the tools available to us.

Let's say that wearing our rose-gold-tinted glasses, we believed that gold had a good chance to make a stand here and climb up to the \$123 area. Now we have to decide which options to use.

First we need to decide on which expiration date to select. There are many dates to choose from, from one week to almost two years. Using options that are too far out will cost a lot of money - the farther out the expiration the more expensive the option. Therefore, going too far out will be a poor allocation of capital. Using options that expire too soon won't work either. If our options expire before GLD makes its move we will lose.

So, we need to estimate how long this move up to the \$123 target could take. We note that the last time that trip was made, between October 2014 and January 2015, it took about twelve weeks. This could be our working estimate of how long that rally could take this time.

Now we need to cross-check against probability. The question now is this: given the recent volatility of GLD, is it reasonable to expect a movement up to \$123 in twelve weeks? And if not, how long should we allow?

To answer this we can use a tool called the Volatility Cone, or Vol Cone. This tool is provided in slightly different forms by several software vendors. The one we're using here is part of the OptionStation Pro package from TradeStation.

To start, we do what is called creating a theoretical option position by selecting an option from the chain. For this purpose we're just going to use an option whose strike price is close to the current stock price and whose expiration is later than our working estimate of twelve weeks. Although our reasonability check is for our twelve-week estimate, we want to add an extra two months to that since we would plan to sell any options that we might purchase when they still have at least two months of life left. That way we avoid owning options in the death-spiral portion of their lives, when time value declines rapidly.

Here is the collapsed option chain for GLD as of March 13, 2015:

Note the highlighted row for the options that expire in 189 days, on September 18, 2015. This is the next available expiration date that is farther out than twelve-weeks-plus-two-months-extra.

Expanding the September option chain, we see:

To create a theoretical position we select an option to be used. In this case I selected the call option at the \$109 strike. This results in the green-highlighted position at the bottom of the OptionStation Pro display above.

Next, we display a two-dimensional graph of the position by selecting the 2D Graph tab at the bottom of the option chain. This is the result:

The top half of the above chart is the familiar option payoff graph which has been discussed in several past articles.

The bottom half is the Volatility Cone. It shows the price range that falls within one standard deviation away from the current price. This is the price range that, given current volatility, has about a 68% chance of containing the actual price at a given future date. It takes into account GLD's Historical Volatility, given as 19.35% at the top of the chart, and then calculates the price that is one standard deviation away as of each date in the future. The vertical axis of the vol cone is "Days Ahead," the more days ahead, the wider the probable range. At the top of the vol cone is the 68%-probable range as of the options' expiration date, 189 days in the future.

The blue labels show that as of the expiration date of 9/18/15, the boundaries of that 68%-probability range are \$96.42 on the down side and \$127.34 on the up side.

Interesting, but not exactly what we want to know. What we want to know is: is our \$123 target probable, i.e. within one standard deviation for a twelve-week time frame?

To determine this we can read down the gold line of the vol curve until we get to the \$123 target price, and then read over from this point to the left axis and read off the number of days. This is a little hard with the fairly compressed scale on the left side of the chart but it crosses on June 25, about 20 days further out then we estimated. We'll need to allow a little more time for our trade to work.

Our example above has to do with GLD, the exchange-traded fund that tracks the price of gold. Here again is the price chart at the beginning of the article:

We were considering a bullish trade based on the demand zone in the \$109-113 area, with a target around \$123. Since that trek took twelve weeks last time it happened, we were estimating a similar amount of time for this trip.

Earlier we created a theoretical option position involving the September \$109 calls, and plotted a P/L graph together with a Volatility Cone. That diagram looked like this:

The gold arc in the bottom half of the chart is the Volatility Cone. As previously described, it indicates a one-standard-deviation price range from \$96.42 to \$127.34 for GLD as of the September expiration date on September 18, 2015.

But what we wanted to know was whether it was reasonable to expect that our target of \$123 could be reached in our estimated twelve weeks. We'll continue to work that out now.

The P/L graph in the upper part of the chart above has two lines or plots. The horizontal axis is the price of the ETF, and the vertical axis is the profit or loss our position (long one September 109 Call) would show for any price of GLD.

By default, the blue plot with straight lines is as of the expiration date, and the gray curved plot is as of today. We can adjust the date of the blue plot forward (closer) until it and its cross-points on the vol cone are as of our twelve-week target date, which would be June 5.

We make the adjustment in the Settings panel, under the 2D Graph Settings section, under Plot 1. We drag the Date slider to the left (to earlier dates) until the date reaches our 12-week target date, which would be June 5. The result is shown below. Note that the blue line is now curved, not straight; and that the legend at the top of the graph now shows a date of 06/04/15 for the blue line.

The blue label on the right-hand cross point in the vol cone now reads \$121.67 which means that the one-standard deviation, 68%-probable range, tops out at that price as of our 6/5/15 target date.

Does that mean that GLD could only go to at most \$121.67 and could not reach \$123 by June 5? Of course not, it just means that going beyond \$121.67 is pretty unlikely, under the assumption that GLD will move in the future with a volatility level that is similar to the recent rate.

If we want to see at what future date our target would fall within a 1-standard-deviation range and, therefore, be more likely to happen, that is easy to do. We just drag the Date slider for Plot 1 further to the right until the cross point reaches our \$123 target. The closest we can get is \$122.94. Here is the graph with that adjustment:

Very faintly, near the Days Ahead axis, we can see that this corresponds to a date of June 25, 2015. This is about three weeks further out than our 12-week estimate of June 5.

What this means is that it would be quite aggressive to expect such a move in 12 weeks, by June 5; but that it would be more reasonable to expect it to happen a few weeks after that. We need to select options that will still have at least two months of life remaining at our new revised target date of June 25. In other words, options that expire in August or later. If we had originally picked options with an expiration date earlier than August, we would now revise our plan.

So, in this case our main decision-making tool, as it always should be, was the location of quality demand and supply zones. Secondarily, we did a probability cross-check with the Volatility Cone which gave us the useful information that we should allow a few more weeks for this trade than we had originally estimated. This kind of information is crucial for options trades since one of our main decision points is the selection of an expiration date.

The Volatility cone has other related uses. For example, say that instead of a directional trade like this one we were contemplating a range-based trade. In such a trade we sell options whose strike prices are outside of a price range within which we expect a stock or ETF to stay for a while. We would identify those strikes, once again, by locating a good demand zone below the current price and a good supply zone above it. The vol cone could then be used to confirm that those strike prices were in fact far enough away from the current price that they were unlikely to be reached by the options' expiration date. Strikes more than one standard deviation away from current price should be the minimum in that case, and more than two standard deviations would be even lower risk (remember that we would be selling options short in that situation and would want any options we sell to expire worthless).

I hope that these articles about probability have increased your understanding of how options work, and how we can use probability to our advantage when trading them.

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