Delta vs. Gamma: What’s the Difference?

It is and always will be debated which option greek is the most important. In fact, there most likely will never be a definitive answer to that question. It may depend on the strategy. Many option traders will refer to option delta as the most important option greek, and that is understandable. I would venture to say most option traders (including myself) learned about delta first. No matter what your thoughts are on delta, however, you can’t dismiss gamma. Option gamma is sometimes referred to as a derivative of a derivative or, as I like to call it, the “common sense greek.”

Option Delta and Gamma

Let’s look at the simple definitions of option delta and gamma. Option delta measures how much the theoretical value of an option will change if the underlying moves up or down by \$1. Long calls have positive deltas, meaning if the stock gains value the option value will increase, all constants being equal. Long puts have negative delta, meaning if the stock gains value the options value will decrease, all constants being equal.

Option gamma is the rate of change of an option’s delta relative to a change in the underlying. In other words, option gamma can determine the degree of delta move. Keeping it simple, for a \$1 change in the underlying, delta will change by the amount of delta. Gamma increases call option deltas when the underlying moves higher and vice versa. Gamma increases put option delta when the underlying moves lower and vice versa.

Delta and Gamma Example

Let’s look at the option chain below. The position is a short (or sold) 190 call with a delta of approximately -0.36 and a gamma of approximately 0.03.

In this example, if a call option is priced at 3.60 and has an option delta of 0.36 and the stock moves higher by \$1, the call option should increase in price to 3.96 (3.60 + 0.36). In addition, the new delta of the short call would be -0.39 (0.36 + 0.03) because of the \$1 move higher.

Positive and Negative Gamma

When you buy options (calls and puts), you get positive gamma. When you sell options, you get negative gamma. Positive gamma helps your delta both ways. In other words, if you have a position with positive delta and positive gamma (long option or positive gamma overall) and the underlying moves higher, the positive delta will increase and the gains will become incrementally larger. If the underlying moves lower under the same circumstances, the positive delta will decrease so the losses become incrementally smaller based on delta. Good stuff both ways.

Negative gamma, in turn, hurts both ways. If you have a position with positive delta but negative gamma (short option or negative gamma overall) and the underlying moves higher, the positive delta will decrease and the gains will become incrementally smaller. If the underlying moves lower under the same circumstances, the positive delta will increase so the losses become incrementally larger based on delta.

ATM, ITM and OTM Gamma

Option gamma is usually highest for near-term and at-the-money (ATM) strike prices and it usually declines if the strike price moves more in-the-money (ITM) or out-of-the-money (OTM). As the stock moves up or down, option gamma drops in value because option delta may be approaching either 1.00 or zero. Because option gamma is based on how option delta moves, it decreases as option delta approaches its limits of either 1.00 or zero.

Final Thought

Based on feedback from MTM students, gamma tends to be one of the greeks (along with vega) that confuse option traders the most. If you consider these simple facts about gamma, it can really improve your understanding of all the greeks. I like to tell option traders that delta is the rate of speed for the position and gamma is how quickly it gets there.

John Kmiecik

Senior Options Instructor

Market Taker Mentoring