Options Lesson I: Gamma Risk by 華爾神偷

delta is a measure of how much the price of an option will change if the underlying stock or index moves 1.00. Gamma is defined as the amount the delta of an option will change if the underlying stock or index moves 1.00. With the SPY at 126.25, the Jan 127 calls had a mark of 1.25, with a delta of .45 and a gamma of .11. If SPY goes up to 127.25, theoretically the 127 call will go from 1.25 to 1.70, which is the delta amount of .45, and delta will go from .45 to .56, which is the gamma amount of .11. Now, that’s assuming that there are no changes in time, volatility, interest rates or yield. If SPY goes down to 125.25, theoretically the 127 call will go from 1.25 to .80, again the delta amount, and the delta will go from .45 to .34, which is the gamma amount. You add or subtract the gamma from the delta for each point that the underlying moves. You must always remember that long calls and put have long gamma and short calls and puts have short gamma. The way I like to think of gamma is that it “manufactures” deltas. Positive gamma manufactures “good” deltas. Negative gamma manufactures “bad” deltas. To explain what that means, let’s look at the SPY 127 call again. With the SPY at 126.25, the delta of the 127 call is .45, meaning that if you are long that call, it will respond to changes in the SPY like it were long 45 shares of SPY stock. I'm interpreting delta here as the stock equivalent position. 45 deltas is directionally equivalent to 45 shares of stock. If the SPY rallies, the positive gamma makes your delta grow to long .56, which means that with SPY higher, the number of long shares of SPY that your call was “acting” like was growing. That means you made more money on the call than the original equivalent stock position. That’s good, which is why I say that long gamma manufactures “good” deltas. If the SPY falls, the positive gamma makes your delta drop to long .34, which means that with SPY lower, the number of long shares of SPY that your call was “acting” like was falling. That means the you lost less money on the long call than the original equivalent stock position. Again, that’s good, and is again why long gamma manufactures “good” deltas.