Diving deeper into the Greeks, we explore a Greek that doesn't measure the move in an option's price, but the move in another Greek. In our Complete Guide To Option Delta, we noted that delta is not a static number, but a number that is constantly changing. To measure that change, we use our Greek gamma. This is where you will learn that not all deltas are created equal. Two options may have the same deltas, but different gammas and different directional risk.
We will explore Gamma; what it means, how it changes based on strike price, time to expiration, and how it changes as volatility changes.
Where To Find An Option’s Gamma
Before we can even begin to define gamma, you need to know where to find the gamma of your options. An option’s gamma, along with the other Greeks, comes out of the option pricing model.
Because Greeks are a byproduct of a calculation, they have a model risk. A model risk is defined as; the outputs are only as good as the inputs. If you plug in the incorrect implied volatility, you can’t expect to receive proper Greeks.
Model risk in terms of option pricing and Greeks is not a serious risk. Out of the 7 factors that affect an option’s price only one of them is unknown: implied volatility. It would be difficult to mess up the model so much that it throws off your Greeks.
It is more important to understand how Greeks are derived and that you can’t always trust the numbers for how they are.
The best place to find the gamma of your option is through an option chain. An option chain displays all the calls and puts for a given expiration and underlying. You can usually customize your option chain to display the various Greeks in which you are interested. Most traders will use their option brokerage, but you can also use free tools such as Nasdaq.com to view an option chain.
What Is Option Gamma
Gamma measures how much the delta will change when the underlying moves $1.
Looking at an example using The Option Prophet (sym: TOP) as our stock of choice:
TOP is currently trading at $50, and you are long the 60 call with a delta of 0.30 delta and a gamma of 0.02. If TOP moves to $51 the delta will increase to 0.32.
If TOP makes another move up to $52 our delta will now be 0.34.
(1(change in price) x 0.02(gamma) + 0.30(delta)) = 0.32
(1(change in price) x 0.02(gamma) + 0.32(delta)) = 0.34
This also works on the reverse. If TOP moved from $52 down to $45 our delta would become 0.20.
(0.34(delta) - 7(change in price) x 0.02(gamma)) = 0.20
Gamma can be positive and negative. All long options, calls and puts, are positive gamma. All short options, calls and puts, are negative gamma.
Gamma, like delta, is not a static number. What measures the movement in gamma you ask? It is a third-order Greek called Speed, the gamma-of-gamma, but you will never need to know that so we will say no more.
Why Is Gamma Important
James Bittman said it best in Trading Options As A Professional, “Gamma answers this question: How much does my exposure to the market change, that is, how much does my delta change, when the price of the underlying stock changes?”. Put more simply, gamma measures movement risk.
How Gamma Changes With Strike Price
An option’s moneyness tells us if it is in-the-money, at-the-money or out-of-the-money. Gamma will vary depending on an option’s moneyness.
The closer your option is to being at-the-money, the higher the gamma will be. As an option moves further in-the-money or out-of-the-money, the gamma will begin to decrease.
How Gamma Changes Based On Time To Expiration
Gamma is affected by the passage of time differently depending on the option's moneyness.
If your option is at-the-money, gamma will increase significantly as you get closer to expiration.
As you get further out-of-the-money, or deeper in-the-money, the effect on gamma is minimized. The further out in time your expiration, the smaller your gamma will be. Gamma and delta will not move around significantly if you have 3, 6, or 9 months left until expiration. Even if your option moves in-the-money, there is still plenty of time for it to move back out-of-the-money.
Let's use an example to understand why this is, and we will also want to remember that delta is our probability of finishing in-the-money. The higher the delta, the higher probability for in-the-money at expiration.
If we have a week left until expiration, and your option is deep in-the-money, it may have a delta of 0.95 (95% probability of finishing in-the-money). Delta cannot go above 1.0 or below -1.0, so your gamma number will be small and won't move around because it simply has nowhere to go, and it doesn't matter.
Now, if you have an option that is at-the-money with one week remaining, your gamma number will begin to increase as the days pass. If your at-the-money option has a delta of 0.50, and suddenly goes in-the-money on the last day of trading, what do you think the delta will become? Remember this is the probability of finishing in-the-money. Your delta could jump up to 0.90 in a single point move. With so little time left, the probability of it finishing in-the-money is substantially higher. This means, your gamma would have to climb up to 0.40 over the last week.
The Gamma Knife Edge
Steven Place coined the term "Gamma Knife Edge" for the affect gamma can have on short traders at expiration.
Short traders will come into the last week of expiration short options that are slightly out-of-the-money. They will want to squeeze every bit of premium out of their positions so they will continue to hold instead of buying back their positions.
The problem, as we discussed, is that if those positions begin to move in-the-money the losses can accumulate very quickly. This often leaves traders stuck with little time, and no way out, but to accept the loss.
The moral of this story: avoid or be careful when you trade short options that are 1-2 weeks away from expiration and close to being at-the-money or in-the-money. It is often best to buy back your positions and collect the profit than have it turn swiftly against you.
How Gamma Changes As Volatility Changes
Studying how gamma moves as implied volatility moves can be counterintuitive.
When we are at low levels of implied volatility, volatility less than 20%, gamma will rise as implied volatility rises.
As implied volatility begins to rise over 30%, gamma will decrease as implied volatility rises. This is where it begins to get a bit confusing.
Remember, when implied volatility increases, it brings our deltas closer to at-the-money, to a delta of 0.50. Therefore, it makes sense that once our options have a 0.50 delta, they are no longer moving as implied volatility continues to increase. If their delta isn’t moving, then neither is their gamma.
We can apply this same logic to options that are already at-the-money. If an option is at-the-money, and implied volatility begins to increase, gamma will not increase. Again, this is because your delta is not moving.
A Gamma And Delta Neutral Position
Getting your position to delta neutral is great, as it makes for a good way to be non-directional. However, as we just discovered, an option's delta moves around almost constantly, making it almost impossible to keep a position completely neutral.
One way you can create a better neutral position is by making it gamma and delta neutral. This will essentially freeze the deltas in place. There are several reasons why people like to do this. When you make a position gamma and delta neutral, you only leave volatility left to move the position around. This will allow you to trade long volatility.
If you have a position that has already made a significant profit but think volatility will continue to increase, say right before an earnings announcement, you can actually take the position to gamma-delta neutral to lock in the current profits but still allow you to profit from an increase in volatility.
Making a position gamma-delta neutral involves a couple of steps. First, you want to establish your base position. Next, you will want to take it gamma neutral. This can be done several ways. Remember that long options are positive gamma and short options are negative gamma.
Once you are gamma neutral, it is time to make the position delta neutral. You simply do this by longing or shorting the underlying position. The underlying will have a delta equal to 1, but it has no gamma because the delta never changes.
Most traders don't actually worry about taking a position delta and gamma neutral. It is usually ideal to trade delta neutral positions without trying to neutralize the gamma. However, it is always good to know that the opportunity exists and how to execute it when needed.
Simply knowing delta is not enough. You must understand how gamma will move your deltas around and thus your position. With this knowledge, you will be able to accurately account for the movement risk in the position.
Be extra careful when trading short options around expiration. If your options are not deep out-of-the-money, it is usually a good idea to take them off the table. Small moves in price, at expiration, can have a big move in the option price.
Taking a position delta and gamma neutral is a good skill to know even though it won't be used all that often in the real world.