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Swim Lessons: A Primer on Option Probabilities

May 25, 2017
Option Probability and Delta
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The following, like all of our strategy discussions, is strictly for educational purposes only.  It is not, and should not be considered, individualized advice or a recommendation. Probability analysis results available in the tools discussed in this article are theoretical in nature, not guaranteed, and do not reflect any degree of certainty of an event occurring.

In our daily Swim Lessons program, co-host Scott Connor and I often refer to some trades and strategies as “high probability,” but what does that phrase really mean?

Probability is generally defined as the likelihood of an event happening, within a certain time frame, expressed as a percentage. With option trades, the “event” may be the likelihood of an option being in-the-money (ITM), and the “time frame” might be the option’s expiration.

So how big does the calculator have to be in order to figure out the likelihood of a certain option being ITM at expiration? Turns out it’s not that hard to calculate. One way is by simply looking at the option’s delta. That’s right! Among the many pieces of information offered by an option’s delta, many traders look at delta an approximate percentage chance that an option will be ITM at expiration. While it’s not a perfect science, it can provide a pretty close estimate.

Ring that Bell (Curve)

Let’s look at some basics. First, if an option is currently ITM, meaning it currently has a delta greater than .50, it’s more likely to still be ITM at expiration. That’s basic probability theory—the price of the underlying stock fluctuates, but those fluctuations tend to be distributed in a way that’s bunched around the current price. Picture a typical bell curve.

Similarly, an option that’s currently out-of-the-money is less likely to be ITM at expiration, And an option that’s right at-the-money? It’s about a coin-toss as to whether it’ll be ITM at expiration, and a delta of around .50 confirms that.

Delta and the Probability ITM Feature

Take a look at the option chain in figure 1. The underlying is at $151.98 so the 145-strike put is out-of-the-money, and its -.20 delta says it has only about a 20% chance of finishing ITM at expiration. Another way of expressing this is to say this option has about an 80% chance of expiring worthless. Hence, selling this option becomes a high-probability trade.

Delta and Probability ITM


TD Ameritrade clients can estimate the probability of an option’s likelihood of being in-the-money at expiration by using option delta or the Probability ITM feature. Source: The thinkorswim® platform from TD Ameritrade. For illustrative purposes only. Past performance does not guarantee future results.

But there’s another way TD Ameritrade clients can estimate an option’s chance of being ITM at expiration: the “Probability ITM” feature in thinkorswim® platform from TD Ameritrade. You can add this to the option chain by clicking on a column header, then Option Theoreticals and Greeks and selecting Probability ITM. While the calculations may be slightly different from the option’s delta, the two readings are generally within a couple percentage points of each other. Either reading can be used to objectively define your risk.

A quick side-note: even if an option’s delta or Probability ITM says 100, there’s no guarantee that the option will actually finish ITM at expiration. There’s always a chance, even a small one, that the underlying could have a big enough move to knock something that’s deep ITM to a position where it’s OTM.

Spread Probabilities

Returning to the example above, suppose instead of selling the 145-strike put outright, you decide to sell the 145-140 put vertical spread. Remember, selling a single put option can expose you to significant risk, but selling a vertical spread limits your potential loss to the difference between your strikes, less the premium you collected, plus transaction costs. For more on selling vertical spreads, read this recent primer.

According to the option chain in figure 1, the 145-strike put has a delta of -.20 and the 140-strike put has a delta of about -.09. So using the deltas as probabilities, we can say there’s about an 80% chance you’ll keep the entire credit, less transaction costs, and about a 9% chance you’ll lose the maximum amount.

So you’d rather use the Probability ITM numbers? They’re about the same, but perhaps slightly less optimistic. The 145 put shows a 21.86% of being ITM, which means it has about a 78.14% probability of being OTM. And there’s about a 10.62% chance of the underlying dropping below $140 before expiration, which again would result in a maximum loss.

These numbers assume that the position is held until expiration. Depending on your objectives, you could close or adjust this trade prior to expiration. But when structuring your trade, and considering adjustments prior to expiration, understanding these probability calculations can help you more objectively manage your risk.

Want more on probabilities? Join Swim Lessons on May 31, 2017 at 10:30 AM CT as Scott Connor  and I dive in further.
TD Ameritrade clients can join Swim Lessons by launching thinkorswim®, and navigating to Support/Chat > Chat Rooms > Swim Lessons > Watch.

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