Books describing how various machinery works were always popular with my girls when they were younger. As options traders, we need to know how our trades work, too.

I decided to choose an underlying and option strategy at random so that we could look at a trade and decide how it would work. Does price need to move big or stay in a tight range? Should implied volatilities rise, fall or stay the same?

Obviously, the example found below should not be considered a trade suggestion. I picked an underlying that had been in the news when this article was roughed out, one that I haven't traded in the better part of a decade. I used a pulldown menu on OptionsOracle to choose the strategy, covering up the choices and picking one at random.

The stock chosen was DD, in the news because it disappointed during earnings. The chosen-at-random strategy turned out to be a put diagonal spread. For newbies, a diagonal can be considered a time spread, when an option in one month is sold and one in another month is bought, usually in a further-out month, "covering" the sold option. The diagonal also has a vertical quality, because the position isn't selling and buying the same strike in those different months. Take a look and see what I mean, remembering that this article was roughed out several weeks ago and these prices are no longer applicable.

Options Positions:

Strategy Summary:

I'll also include a profit-and-loss expiration chart, so if you don't know anything or want to know anything about the Greeks of a trade, you may want to skip to that graph.

First, you should know that the then-current price of DD when the options were chosen was $44.91, and it was October 24, 2012. The price had jumped to $45.25 by the time the Strategy Summary chart was snapped. By the time the Strategy Summary chart was snapped, the trade was already showing a profit of $26.50, visible under "Current Return." Under the "Criteria" column, we see an entry for "Maximum Profit Potential." That occurs at $47.00, according to this table, and that's above the then-current $45.25 price. This was obviously a bullish trade, one that would benefit from a climb to $47.00. "Lower Protection" is at $44.23, with this term being another term for the expiration breakeven.

The chart offers another way of determining right away that this is a bullish trade that will benefit if DD rises: that's the delta. Delta is positive, at 25.75. For those not familiar with the Greeks of options trading, delta measures how much the value of the position theoretically changes with a 1-point move in the underlying. Of course, that explanation doesn't tell the whole story because other factors can be impacting the price of the position while the underlying's price rises. Because delta is positive, the position's value theoretically increases when DD's price increases, at least up to $47.00.

The position is also positive theta, if only mildly so. For those not used to Greeks, theta measures how much the position benefits or is harmed by the passage of time. At least for the time being, this trade benefits $2.08 each day, at least for the immediate time period.

This is also a positive vega position. For those not used to the Greeks of option pricing, vega measures how much a position is helped or hurt by an increase in volatility. In this case, vega is positive, so each 1 percent the implied volatility of the options rises, the position theoretically gains $4.15.

From looking at this chart, then, we know that anyone with this position can lose 100 percent of the investment (margin plus estimated commissions, in this case) in the position, but will benefit from a climb in price, a passage of time, and a rise or steadying in implied volatilities. A fast gain would be good since it would keep implied volatilities steady or even bring them higher, while a slow and steady rise sometimes drops implied volatilities. Now let's look at an expiration chart.

Expiration Chart:

The red dot is positioned at DD's then-current price. If DD's price were to decline below the expiration breakeven, the point at which the blue expiration line crosses below zero, losses would steepen until they began flattening at the maximum loss. If DD climbs, the profit would climb and then top off. You'll notice that the expiration breakeven curves lower again beyond 47. In fact, you'll notice several curving lines in this expiration graph. Whenever you see curves in an expiration graph and not straight lines and angles, you know that the position is composed of options in more than one expiration cycle.

Implied volatilities tend to rise when there's been a sharp decline, and DD had gapped down and driven lower that week. We can assume that we were selling an option with high implied volatilities and an inflated price. But had implied volatilities risen on the long JAN option? On another chart, freeware OptionsOracle tells me that the mean for the JAN period's options was 19.27 percent with a low of 13.51 and a high of 34.45 percent. That's not information I verified independently, but let's take it as factual for the purposes of this article. At the time of the article, the JAN option's implied volatility was 21.37 percent, so somewhere in the middle of the range. The November option's implied volatility was 36.32 percent, definitely impacted.

So what happens if, over the course of the next two days, by October 26, DD rose to test $46.00, a level that had been prior support for many months? Perhaps some of that pumped-up implied volatility would leak out of the trade, too. Two days would have passed. Let's imagine that implied volatilities dropped by 3 percent. So, according to the Greeks, we would expect gains for this position of [(46 - 45.25) x 25.75] + 2 x 2.08 + (-3)(4.15) = $11.02 to be added to the current $26.50 profit. That makes the theoretical profit $37.52. This is approximate because it ignores gamma effects, for example.

For those who prefer looking at a chart, let's look.

Profit-and-Loss Chart for October 26, with Lowered Implied Volatilities:

The profit-and-loss chart shows a gain, but it's more than the gain we expected, $82.01 instead of our expected amount. Why the difference? Here's where I wished my blind choice of a strategy had returned anything other than a time spread, but at least it gives us a chance to talk about the benefits and shortcomings of any type of modeling system.

Any modeling system has strengths and shortcomings. Modeling systems can help you position your trades so that they act as you expect them to act, but only if you understand the shortcomings.

I thought I knew what might be happening, so I checked on think-or-swim (TOS). TOS returned a potential profit of $83.06. The two charted estimates are fairly close, despite differences that showed up in the initial deltas of the trade.

So, what's up with these inflated profit predictions when compared to the calculated one? With TOS, I don't use the default "individual volatility" setup. I use a "volatility smile" approximation that will take into account the way options' implied volatilities might change as price moves closer to or away from the strike price of the options involved. For those of you who know the word, this approximation makes some effort to account for the skew of the options. In most options cycles, that skew is a kind of a smile, either a rather sedate, flattish smile or a turned-way-up-at-the-corners smile. The smile is created because out-of-the-money options, especially OTM puts on equities, tend to have inflated implied volatilities.

Since the two choices returned such similar theoretical values, I would guess--although it's just a guess--that OptionsOracle does something similar to the "volatility smile" approximation on TOS. When I return to TOS's default "individual implied volatilities" setup, the theoretical profit returned under our set of parameters was $56.72 (minus commissions). That's lower than the previous graphed estimations but still higher than anticipated by our Greeks calculations.

Which estimate is right? Maybe neither is quite right. When you're dealing with options in two widely separated options cycles, the implied volatilities can move independently of each other. It might be that the implied volatilities in the November cycle will drop out quickly if DD settles, perhaps dropping 6 percentage points, while the January cycle drops only 2 or 3 percentage points because there's some uncertainty about the next earnings cycle. The model used, the complexity of a time spread, gamma effects for which we haven't accounted: all can change the actual profit or loss from what we expected.

Still, I can't repeat enough how valuable these models can be. They allow you to experiment, and find out how these changes impact your trade, even if the theoretical profit or loss turns out not to be exact. In fact, I can guarantee that it won't be exact. It's up to you to learn through experience how your model, your underlying and your strategy the model will go wrong. Only lots of experimentation will teach you that. If I were planning on trading diagonals with some frequency, I would also certainly be calling tech support on my preferred platform to ask them how the model made predictions. The nitty gritty information is likely to be proprietary, something that developers might not be willing to share. However, they usually can answer at least some of your questions and point you to the best way to model the position you want to model.

Perhaps you prefer to watch a spreadsheet with the Greeks recalculated and new PnL projected at regular intervals. It's my understanding that floor traders, specialists and market makers usually watch via some kind of spreadsheet setup rather than these kinds of analyze charts. Perhaps, like me, you like to watch charts. Whatever way you prefer to do so, learn how your trade will gain and lose, and what a mixture of effects of changing implied volatilities and price and the passage of time will do to the trades. We haven't had to worry about rising rates in a long time, but when we get into a cycle when interest rates are raised again, you'll have to add that parameter in, too.