While few of us in modern civilization have worked bellows, we've certainly seen them. We know how they expand and contract. Keep that image in mind while we think about the way that volatility impacts our options trades.

Let's imprint that image. We'll start with an options trade that has a tent-like shape that can also be said to resemble bellows: the butterfly. With the OEX at 474.77 on August 26, 2010, we'll construct a single contract of an at-the-money 450/475/500 September call butterfly.

Expiration Profit/Loss Chart for OEX September Call Butterfly:

However, it's not the expiration graph that's most important to us in our day-to-day trading of a butterfly or other complex strategy. We're concerned about what's going to happen to our trades over current day or next few days.

For example, the graph below shows the potential profit or loss two weeks after this trade was initiated if volatility remains the same. The upside breakeven point on that day would be at 489.24, the site of the red circle.

Theoretical Profit/Loss Chart for OEX SEP Call Butterfly on 9/9/10:

The butterfly is a vega-negative trade. Theoretically, it performs better if the volatility contracts. Let's see what happens to upside breakeven point as of September 9 if volatility falls. Our bellows or tent-shaped image has disintegrated a bit on this "today" graph. However, it's still possible to see that this is a shape that might expand and contract. That's especially true if we concentrate on the portion above the zero line that marks the difference between profit and loss. Let's watch to see if any contraction or expansion of the bellows occurs when volatility drops. If we expect a vega-negative trade to perform better when volatility drops, then we expect the portion of the bellows above the zero line to expand, don't we?

Theoretical Profit/Loss Chart for OEX SEP Call Butterfly on 9/9/10 with Lowered Volatility:

The red dot is now at 491.36, the new upside breakeven point. The bellows has expanded a bit. You might also notice that the maximum profit on that day has risen, also. Unlike real-life bellows, this one has expanded both in width and height.

What happens if the volatility rises, an event that should hurt the theoretical profit results on a vega-negative trade?

Theoretical Profit/Loss Chart for OEX SEP Call Butterfly on 9/9/10 with Raised Volatility:

The new upside breakeven, with higher volatilities factored in, is now 488.30, and the peak of the graph is lower, too, showing less possibility for profit on this particular day.

The calendar, unlike the butterfly or the iron condor, is a vega-positive trade. This trade theoretically benefits from a rise in volatility. This is a bit of a simplistic view when it gets down to real-life trading. The two different expiration periods that make up the calendar's options trades complicate matters a bit. Changes in volatility don't always impact the two sets of options similarly. However, if one surmises that volatilities would drop or rise fairly evenly across the different expiration options, one would expect the calendar to react the opposite of a butterfly. That bellows would widen when volatilities rise and contract when it dropped.

First, we begin with a view of a calendar trade in place for two weeks, with no change in volatilities.

OEX SEP/OCT Call Calendar After Two Weeks, with Static Volatilities:

The upside breakeven at the red dot is 523.55. With volatilities raised, we would surmise that the bellows would widen and the upside breakeven would be further out.

OEX SEP/OCT Call Calendar After Two Weeks, with Raised Volatilities:

In fact, that's what we do observe. The new upside breakeven is 526.87 and the potential profit at the peak is higher, also.

As mentioned earlier, the bellows observation isn't entirely correct since the top, or maximum profit, also changes. Perhaps a sinking or rising iceberg analogy might be more appropriate. The iceberg rises higher and widens or sinks lower and narrows with changes in volatility, depending on whether we're looking at a calendar or butterfly trade. I like the bellows analogy because it's such an easy image to remember. This helps us remember that if volatilities are expanding, a butterfly or iron condor might need to be adjusted sooner rather than later, and a calendar might need to be adjusted later than it would have previously.

Of course, I've used upside breakevens in my examples here, but these expanding and contracting graphs work somewhat the same way when considering downside breakevens. Whatever image you use to help you remember the effects of volatility on a trade, we're reminded to keep volatility in mind when we're planning adjustment points. We must remember, too, that the different expirations of the options composing calendar trades complicate matters a bit, especially in equities that might be facing earnings or another important event before the expiration of one of the other of the options. I wanted readers to realize what changing volatilities can do relatively early in their trades so that they could prepare to react appropriately, not promise that each trade will react as anticipated in each eventuality.

Of course, if one does hold a trade into expiration, volatility in the front-month options will quickly collapse toward zero and be of less concern. Other Greeks, such as delta, gamma and theta become more important, at least with the front-month options.