Delta

W What does delta measure?
Delta measures the rate of change of an option's price given a plus or minus change of $1 in the underlying price. Delta answers, "If the underlying increases or decreases by $1, by how much will the option price increase or decrease?". For us math nerds, delta can be thought of as the derivative of an option's price. 

Option Price Deltas
Option price deltas range form -1.0 to +1.0. If an option price has a delta from -1.0 to 0, it has a negative delta. If an option price has a delta from 0 to +1.0 it has a positive delta. Positive and negative deltas are important in assessing our directional assumptions regarding the options transactions. Let's take a look:

Options Transactions and Delta Signs

• Buy Call : Bullish, option price increases as underlying price increases -> Positive Delta
• Sell Call: Bearish, option price increases as underlying price decreases -> Negative Delta
• Buy Put: Bearish, option price increases as underlying price decreases -> Negative Delta
• Sell Put: Bullish, option price increases as underlying price increases -> Positive Delta

A positive or negative delta, as implied above signifies a directional assumption, and therefore risk. A positive delta, such as a in the case of buying calls or selling puts assumes a long market, whereas a negative delta like those of selling calling and buying puts assumes a short market. The sign of a delta assigns a directional risk to our overall positions. In order to reduce our risk, it is preferable to keep deltas neutral or as close to 0, so as to avoid the association of an underlying's direction to the fate of our positions. 

Delta Benefits 
An option's delta is equivalent to the probability of being ITM. As established earlier, sellers want the options they've sold to expire ITM in order to profit. Therefore, sellers can use deltas to assess the probability of ITM. Similarly, buyers can use deltas to assess the probability of the option expiring OTM (where they profit). For example, if we sell a + 50 delta call, there is 50% chance the option will be ITM, and a 50% the delta will be OTM. What if the delta is negative?  If we sell a -30% delta call, there is 30% of the option expiring OTM and therefore a 70% of the option expiring ITM. 

16 Delta
You might often hear of the mysterious "16 delta". What does this even mean? If we look at a one standard deviation move on the traditional bell curve, the distance from the mean is 34% on either ends. The width is approximately 68%, leaving 16% percent flaps near each tail end. If we sell a -16% delta call, this means we have an 84% (16% flap we mentioned earlier + 68%)  chance of the option expiring ITM (success!). This is usually the sweet spot we like to look for when trading.