I’m not a huge baseball fan – I live in Chicago and root for the Cubs so I’m used to disappointment. But this week is the final home game for Derek Jeter and even I will pay attention. With all the garbage being spewed out of the NFL in the past couple of weeks it’s nice to see a guy like Jeter get center stage. 20 years with the Yankees. Class act his whole career. TMZ never sprung a story about him. So farewell number 2. Enjoy retirement.
Last week we went over how changing volatility affected delta. This week let’s cover delta’s nasty step sister – gamma. The reference really points to the fact that gamma seems to be the least intuitive and most difficult of the greeks to understand. First let’s review what gamma is.
Gamma is how much delta changes over a given change in underlying price. For example, if XYZ moves up $1 and gamma is 2 then delta would move from say 40 to 42. For the mathematical inclined it is the slope of delta. So the slope is what it is under a “normal” volatility environment. But say vols blow up – back up to 80 in the VIX like last week. What happens to gamma? Well that depends.
Remember, as vols rise, all deltas tend to move toward 50. For the strikes at the money and nearby gamma drops as vols rise. If those deltas are close to 50 then deltas are not moving much so gamma can’t be big. What about the strikes away from the at the money?
If you remember from last week an increase in IV pumps some life into the far in the money and out of the money strikes so that area might actually gain some gamma. Higher vols mean maybe those strikes can end up in or out of the money after all. And where gamma was nil for some dead option that no one thought would see the light of day now it has some life and hence some gamma. So the bottom line is this – higher vols mean lower gamma as you move toward the at the money. As you move more away from that strike the gamma may gradually increase relative to those lower strike, lower vol gammas. Gamma tends to get more flat across all strikes as gamma increases. Now quit reading and go outside.