by Tyler Craig | March 30, 2012 12:43 pm

[1]As a self-professed options addict, I’m always on the lookout for items in pop culture or everyday life that have relevance to my trading ventures. During my viewing of the recently released blockbuster *The Hunger Games*, I was pleasantly surprised to come across a slogan that could very well have turned up in an options manual.

*“May the Odds Be Ever In Your Favor”*

While the phrase was a motto of sorts for the denizens of the nation Panem, it could very well be a motto for the option sellers among us. Most of these traders look to have the odds in their favor by structuring positions with a high probability of success.

In order to inject probability analysis into the mix, traders must first understand how to use the Greek delta. The property of delta that interests us in this discussion is its ability to gauge the probability of an option expiring in the money. Suppose you purchased a May 50-strike call with a delta of 75. The delta tells you there is a 75% chance the call will reside in the money at May expiration. Put another way, there is a 75% chance the stock will be trading above $50 when that series of options expires.

Now, let’s say you purchased a May 70 strike put with a delta of -30. This tells you there is a 30% chance the put will reside in the money at May expiration. In other words, there is a 30% chance the stock will be trading *below* $70.

Add a dash of intuition to the aforementioned principle and you will also be able to calculate the probability of an option expiring *out* of the money. Simply put, if delta equals the probability of an option expiring in the money, then 1 minus delta equals the probability of an option expiring out of the money.

Suppose with the USO trading at $39.50, you short a May 37 put option, which has a delta of -27. Given the delta value, there is a 27% chance the put option will sit in the money at expiration. So what are the odds the put expires out of the money, thereby allowing you to capture your max profit? Using the 1 minus delta formula, outlined above we arrive at a profit probability of 73% (1 – 0.27).

This unique usage of delta allows option sellers to select the optimal strike price to achieve their desired probability of profit. If they’re looking to increase the likelihood of capturing a profit, they simply sell lower delta options.

An important side note is that modifying the probability of profit also changes the potential risk and reward of the position. This, however, is a discussion for another day.

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