Gamma is the Greek that quantifies the change of Delta. For information about Delta, see the webpage on Delta.
Gamma is defined as the amount of change to Delta that will occur from a one dollar change in the underlying security price. Gamma is positive number between 0 and 1.0, generally very close to 0. If price goes up a dollar, add Gamma to the previous Delta to determine the new Delta. For this to work, you have to use positive and negative Delta decimal values.
For example, consider an at the money call and put each having a 50 Delta (actually 0.50 and -0.50). Let’s assume the Gamma value for each is 0.04. The underlying goes up one dollar, and the put goes out of the money and the call goes into the money. The new Delta value for the call is 54 (0.50 + 0.04), and the new Delta value for the put is 46 (-0.50 + 0.04). So, for the math to work, you have to keep track of the positive and negative signs of Delta.
There is one key thing to know about Gamma that isn’t obvious at first. Gamma gets bigger as you get closer to expiration. As expiration approaches, the market expects the underlying to trade in an ever-smaller range of outcomes at expiration. Because of this, only options that are close to the underlying price have time value left. If prices change suddenly near expiration, Delta will change large amounts. Gamma is the measure of that change in Delta. Gamma risk is what makes managing positions close to the money near expiration very risky and unpredictable. To be fair, Gamma isn’t a villain, it’s just a measure of how quickly prices can accelerate for or against you.
If you think of Delta as the velocity of option price changes, Gamma would be the acceleration- the rate of change of the rate of change. If that analogy doesn’t make sense, you probably didn’t study Physics or Calculus. In Calculus terms, Delta is the first derivative of option pricing and Gamma is the second derivative. Fortunately, you don’t have to know Calculus or Physics to utilize option Greeks.
For different options on the same underlying, Gamma can be combined to determine the gamma of a combination of options. Adding an appropriate out of the money position can make a position Gamma-neutral, which is more stable than simply Delta-neutral. Most of the time this really isn’t a consideration, but calendar spreads in particular can benefit by adding a Gamma hedge.
Gamma has significant limitations in how it can be combined between positions. Like Delta, it needs to be price weighted to get a value for a variety of underlying securities. There are few practical reasons to attempt to combine it between multiple positions, since it is a derivative of a derivative. It can be useful for comparing different positions to make a decision to roll from a high Gamma position to a lower Gamma position, but generally other Greeks provide more understandable portfolio and risk management indications.
To be honest, I don’t pay much attention to Gamma, because it just does its thing to Delta as prices move, and I watch Delta. I know that Delta moves more quickly as expiration approaches, and for most situations, that’s enough for me.
