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Using an Options Delta for Probabilities

Good ol Delta. Options traders use it for everything: from measuring premium movements to notional sizing. We can also use it for a rough probability approximation of being ITM or a touch. This is because of the way delta is calculated in comparison to probability calculations. They are NOT the same but they are similar. What you'll find, is in general, for shorter term options (within a year) the variance between delta's probability approximation and actual probability calculations are fairly similar (<10% difference in most cases).

For an in depth review, checkout this video:

For example, let's look at AAPL:

  • This is the 11Feb expiration (5DTE from the time of writing). We see the -0.35 delta 170P has an approximate probability of being ITM (PITM) at expiration of 35% and a 70% probability of a touch.

  • Actual PITM calculation is 36.02% with a 71.03% probability of a touch

  • This puts us at a 1.02% variance for PITM and 1.03% variance for touch

Now, let's go further out in time:

  • This is the 20Jan23 expiration (348DTE)

  • The -0.35 delta 160P has a 35% approximated PITM and a 70% probability of a touch

  • Actual PITM is 46.41% with a 83.14% probability of a touch

  • This is a 11.41% variance for PITM and 13.14% variance for touch

Using delta is a great back of the napkin tool for PITM and touch, but it's important to understand how it behaves. I have a video coming out soon that goes into a deep dive on how different variables affect delta. In the meantime, to summarize the primary reasons we see this is a mix of the time premium in the options (attributed to volatility).

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