What About Gamma ?

Gamma

Gamma's sole purpose is to affect the Delta. It can either be friend or a foe to Delta.

As we have discussed, Delta, is the greek that determines the amount of change to the option price, when the underlying moves by a point.

Then, you will understand when Gamma is defined as the Delta's delta; ie, Gamma determines the amount of change to Delta when the underlying moves by 1 point. If delta is a the 1st derivative then the gamma is the 2nd derivative. If delta is velocity, then gamma is acceleration.

Let's look at Visa (V), currently trading at $71. The current option chains are shown below.



A Long 70Call has a delta of 0.56 and a gamma of 0.08. If V rallies up $1, then 70Call delta will change to 0.64 (0.56 + 0.08). If V drops by $1, the same option's delta will also drop to 0.48 (0.56 - 0.08).
So, it is clear that Gamma has a direct impact in the value of the option's delta. The more +ve Gamma that option position has, the bigger the movement of value option's price will swing.
This is the reason that when Long OTM Call positions are very unreactive to underlying price movement. The V example shows this.
Look at 80Call option, this is OTM Call. It has a delta of 0.04 and a corresponding gamma of 0.02. Even if V rallies from $71 to $72 now, the 80Call delta will only be increased to 0.06 (0.04 + 0.02), which translates to a 6 cents movement in 80Call value. Obviously, this OTM Sept80Call isn't worth much now; about 7.5cents and has only a 4% chance that it will become ITM by 8 days time, when this option expires.
Do you remember how we conclude that this OTM80Call has only 4% chance of getting ITM? If not, you should re-read the post on Delta.

Now for the confusing part.

Supposing you had Long V 65Call which has now a 0.82 delta and 0.04 gamma. But imagine, for some reasons, your gamma was -ve 0.10. This can happen when you have multiple option positions of the underlying, that results in a +ve delta and a -ve gamma.
If the position has a NET +ve 100 delta, supposedly, you would want the stock to rally, since a NET +ve delta is a bullish position and will be profitable only when a rally occurs. BUT, the overall gamma of this combined positions, as stated was -ve 20. Then in a 1 point rally, your delta will be reduced to +ve80 (100 - 20). This is no good. Of cos, as the stock rallies up $1, you will still make that $100 (from the initial 100 deltas), but supposing it now rallies another point, from $72 to $73, effectively, you additional profit is only $80. You will still be making money, just not as much. What is responsible for this mess up? Gamma, of cos.

Similarly, in any bearish position, where the delta is -ve, you will want to gain delta as time passes. In this case, gaining delta for a bearish position, means making the delta more "-ve"; as in -0.9 is better than -0.2. This is the tricky part; so pay attention. You will still want a +ve gamma for a -ve delta position. It is not intuitive, but it is correct notion. A +ve gamma will make a -ve delta more -ve , when the price of the underlying drops.

Another way of looking at Gamma, is to think in terms of Volatility. If you were Long or Short a position, you certainly want price action, don't you? Afterall, a stationary market will slaughter all single directional bets, like Long Call and Long Put. Hence, when you have such positions, you want Gamma to be as gigantically +ve as possible.

But, if your option strategy is for the quiet market, then you want -ve Gammas to "tame" those deltas, and even making them as small as possible..

Hence, option writers (stationary or non-volatile option positions; such as Short Strangle or Short Straddle), will want -ve gammas in their option portfolio....

If you look carefully at the option chain above, you will see that gamma is largest for ATM options. This is always the case. The reason is very simple. At expiration, all ITM Call options will have delta +1 and all OTM Call options will have 0 delta. Similarly, ITM Puts will have -1 delta and OTM Puts will have 0 delta.
Now, we are 5 minutes away from closing bell of expiration day. V is trading at 74.90, the 75Call has a good chance of being ITM and is now 0.25 delta. One second passes and V trades 75.05, this 75Call's delta immediate jumps to 0.89. See the movement of delta from 0.25 to 0.89. That huge change is caused by Gamma. Hence, all ATM options has the largest Gamma.

so, in summary, this is how these 2 GREEKs interact with Calls and Puts

.................................................Delta....................Gamma

Long Call..................................+ve...........................+ve
Short Call.................................-ve............................-ve
Long Put..................................-ve............................+ve
Short Put.................................+ve...........................-ve