Before I answer, I should warn anyone who is new to options trading that understanding my answer to this question requires you to already have a basic understanding of options.

The truth is, all calls and puts don’t have the same Gamma. So a better way to ask the question is “Why do calls and puts with the same exercise price and time to expiration have the same Gamma?”

The answer? Because Gammas influence Deltas of calls and puts in the same way, expressing their probability of finishing in the money after a change in price in the underlying.

Bear with me and I’ll try to explain my answer from a couple different angles.

Characteristics of Gamma

Let me start by pointing out an important characteristic of Gamma that is critical to understanding the answer. All long options (either calls or puts) have positive Gamma, while all short options have negative Gamma. This is quite different from Delta, right? Long (short) puts have negative (positive) Delta. Long (short) calls have positive (negative) Delta. With Delta, traders get so used to associating negative numbers with puts and positive ones with calls that working with Gamma can seem awkward.

Gamma is a 2nd Level Derivative

Remember that Gamma is a 2nd-level derivative — in other words, a derivative of a derivative (Delta). People often define Gamma as “the rate of change of Delta,” which means it measures how fast an option changes its directional characteristics. In other words, it essentially measures the degree to which an option acts like the underlying.

Imagine you are long an at the money call with a .50 Delta and long an at the money put with -.50 Delta (aka, a long straddle). Also understand that the Delta is roughly the probability of the option finishing in the money, so both of them are currently at a 50% probability. Let’s assume both have a Gamma of .10.

• The underlying moves up $1, which means the 10 Gammas are added to the Deltas of both the positive Delta calls and the negative Delta puts.
  • The calls move into the money and their Delta goes to .60, which:
    • Acts more like the underlying
    • Reflects a higher probability (~60%) of finishing in the money
  • The puts move out of the money and Delta also goes to -.40, which:
    • Acts less like the underlying
    • Reflects the worsening probability (down to ~40%) of finishing in the money

What Happens When You Add Gamma?

See, you add the Gammas to both calls (which have a + Delta) and puts (- Delta) when the underlying goes up, or subtract it from both if it goes down. Adding the Gamma from both calls and puts with the same strike and expiration accurately reflects the “teeter totter” effect we get when probability for the calls finishing in the money goes up by 10% and the put probability goes down by 10%, assuming the underlying went up $1 as it did in this example.

I must point out that my example (and the question) assume  interest rates are zero. If carry cost from interest rates or some other reason presents a possibility for an early exercise in an American style option, then Gammas may differ between calls and puts of the same expiration and strike.