Why is gamma the same for call and put options?

[JBgroove]

???????

[StoneF]

I'm not sure that I can explain it clearly but I'll give it a try.

As the underlying moves up, a call's delta heads toward 100 as the put's delta heads toward zero. As the underlying moves down, a call's delta heads toward 0 as the put's delta heads toward -100. IOW, as the underlying increases, the put delta put moves from -100 to 0 as the call moves from 0 to 100 (and vice versa as the underlying drops). If you look at the graphs and compare same strike/expiry puts and calls, you'll see that they are almost identical so as price increases, both gammas increase equally. The P&L outcomes are different, not the gamma.