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Decisions, Decisions: Understanding Option Probabilities

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March 29, 2018
Option Probability and Delta
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Options trading, like all investing really, is about decision making: weighing the potential reward against the potential risk, and the probabilities thereof.

But isn't that life in general? By some estimates, the average human makes 35,000 decisions in a typical day. Whether you believe that statistic or not, let's just agree that we make a lot of decisions every day. In general, these decisions are about risk and reward or, in other words, weighing the probabilities:

  • Should you cross the street now, or wait for that approaching car to pass?
  • Going with the salad for lunch today, or is that slice of pizza calling your name?
  • Should you sell a call option against a stock in your portfolio, and if so, which one(s) should you consider?

Probability and Option Delta Definition

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) or out of the money (OTM), and the time frame might be the option’s expiration.

Turns out, with the right tools, 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 as an approximate percentage chance that an option will be ITM at expiration. Although it’s not a perfect science, an option delta calculation can provide a pretty close estimate.

Delta and the Probability ITM Feature

Take a look at the option chain in figure 1 below. The underlying stock is trading around $175.50, so the 182.5 strike call is out of the money, and its 0.20 delta implies 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. 

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

Delta and Probability ITM

FIGURE 1: OPTION CHAIN WITH DELTA AND PROBABILITY ITM.

TD Ameritrade clients can estimate an option’s probability 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.

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 in the money at expiration. There’s always a chance, even if it's 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 that instead of just selling the 182.5-strike call outright, you decide to sell it and also buy the 187.5-strike call (in trader parlance, this would be "selling the 182.5-187.5 call vertical spread"). Remember, selling a single 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.

According to the option chain in figure 1, the 182.5-strike call has a delta of 0.20 and the 187.5-strike call has a delta of about 0.07. 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 7% chance you’ll lose the maximum amount.

So you’d rather use the Probability ITM numbers? They’re about the same, but perhaps slightly more optimistic. The 182.5 call shows an 18.37% chance of being ITM, which means it has about an 81.63% probability of being OTM. And there’s about a 6.25% chance of the underlying rising above $187.50 before expiration, which again would result in a maximum loss.

Applying the Math to Decision Making

These numbers assume that the position is held until expiration. Depending on your objectives, you could try to 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.

Comparing an option's delta (or other probability calculation) against the price at which you could buy or sell an option can help you determine your strategy for entering and exiting option trades. And with that decision out of the way, you can move on to other important matters, such as whether to have the salad or the pizza for lunch. For that decision, though, you're on your own. 

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Let’s look at some basics. First, if an option is currently trading at a price that's ITM, meaning it currently has a delta greater than 0.50, it’s more likely to still be in the money at expiration. That’s basic options 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 a coin toss as to whether it’ll be ITM at expiration, and a delta of around 0.50 confirms that.

Delta and the Probability ITM Feature

Take a look at the option chain in figure 1 below. The underlying stock is trading around $175.50, so the 182.5 strike call is out of the money, and its 0.20 delta implies 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. 

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

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