Our last article, "Option Deltas - The Basics," ended with a promise to explain a model options traders sometimes use to understand option deltas and how they change. This article will explore how to use the probability of finishing in-the-money to understand how option deltas work. While this model is by no means exact, it is a handy mental shortcut to aid one's understanding.

Before diving in, we should discuss the way traders talk about delta in different contexts. When talking about positions, traders usually speak in terms of their chosen unit. It would not be uncommon to hear a trader say something like, "This rally has me long about ten deltas up here." Meaning the delta of the trader's position has changed to being long ten units because of the rally. In the grain and soybean markets, the standard unit is often equivalent to futures contracts. So, it would be normal to hear "deltas" and "futures" used interchangeably in this context. In this case, the trader is talking about his position's overall exposure. He is not necessarily referring to actual futures contracts he holds. Instead, he is explaining his total exposure in equivalent futures contracts. When talking about individual options or spreads, traders typically use the percent of one underlying contract that the option represents. You might hear a trader say something like, "I have too many ten-delta calls in my position." Meaning the trader is unhappy with how many 0.10-delta calls he owns. We will use these conventions as we move forward with this article.

To start, we need a baseline for our model. That baseline is this: At-the-money options have an absolute delta of close to 0.50, or in trader speak, "fifty-delta." That should be somewhat intuitive. There are roughly equal probabilities at-the-money options will finish in or out-of-the-money. We can extend this reasoning further. The more in-the-money a put or call is, the more it is likely to stay in that way, and the more out-of-the-money it is, the more likely it is to stay there. So the deeper an option is in-the-money, the closer its delta gets to an absolute value of 1.00. The further it is out-of-the-money, the closer that option's delta is to 0.00.

When things start to move around in this model, individual option deltas generally move in two primary ways. They get more or less positive or negative, or they can move closer to or further from an absolute value of 0.50. By applying that thinking to how various input changes affect the probability of finishing in-the-money, we can get a good sense of how an option's delta will change.

Suppose the market drops. Puts are now more likely to finish in-the-money, and calls are now less likely to do so. So, put deltas will move toward negative-one, and call deltas will move toward zero. The reverse will happen in a rally. That means the overall directional exposure of a trader who owns options will become longer during rallies and shorter when the market falls. The opposite will happen for writers of puts and calls. This process is called "gamma" in the options trading world. Gamma is a topic we will cover more deeply in another article.

As we mentioned in "Option Deltas - The Basics," price is not the only factor that affects an option's delta. Time to expiration has a significant impact on an option's delta as well. If we continue to use the probability-of-finishing-in-the-money model, we find some noteworthy results. As the time to expiration increases, option deltas move toward an absolute value of 0.50. Think about it this way. Given more time, out-of-the-money options have more time to become in-the-money, while in-the-money puts and calls already have more time to move out-of-the-money. The opposite happens as the time to expiration decreases. Effectively, the more time we are dealing with, the more uncertainty there is, and the more things start to look like the flip of a coin.

Like time, volatility expectations also have a significant impact on option deltas. Volatility expectations are crucial because they tell the model how much uncertainty to expect for a given unit of time. Different types of traders might use various volatility estimates in their models, depending on their goals. Hedgers typically use the market's implied volatility as a guide because hedgers tend to believe the market knows best. Covering the different types of volatility and reasons to use one or the other could fill a book - we will get to that in future articles. For our purposes here, whatever volatility expectation one is using, if that expectation increases, it will have a similar effect on option deltas to increasing time. That is, as volatility expectations grow, option deltas move toward an absolute value of 0.50. The opposite will happen as we decrease volatility expectations. Again, the more uncertainty there is, the more things start to look like the flip of a coin.

Most of the other factors that affect option deltas are fixed (like the type and strike of the option). Still, others like those associated with cash flows usually have minimal impacts on option deltas. That is especially true in the grain and soybean market, where dividends are not a factor. Remember, the ultimate goal here is to understand how options will perform in a hedge portfolio. To design an effective hedging strategy, like the one at the heart of Quartzite Precision Marketing, we need a good understanding of how the individual components will perform. It is worth noting that some academics will likely take issue with this article. We intentionally left a lot out. Here, the purpose is to convey a rough conceptual understanding of how input changes affect option deltas, not a definitive one. We hope this article helps with that. Our goal is to present useful information in an understandable format. As always, we look forward to your questions and feedback.