Delta vs Gamma

The rate of change of an option's price relative to a $1 change in the underlying asset price; ranges from 0 to +1 for calls and -1 to 0 for puts; ATM options have delta approximately ±0.5; delta is also used as a proxy for the probability that the option expires in-the-money.

The rate of change of delta relative to a $1 change in the underlying price; highest for at-the-money options near expiry; long options have positive gamma; short options have negative gamma; high gamma positions are unstable and require careful management near expiry.