Gamma

[00:00:00.14] - Speaker 1
What is the Gamma of an option? We will see it in this lesson. Gamma is defined as the change of delta of an option for a unit change in the price of the underlying. Assuming constant other factors, the delta of an option as we know changes according to the change of the spot price. Gamma is the change in Delta for a 1% change in the spot price.

[00:00:19.23] - Speaker 1
If we want to simplify, the Gamma is the speed at which the Delta moves. Gamma is also one of the reasons why the market maker is forced to Delta hedge with the change of the Delta. Here we can see the main chart of our QModas that we send to our subscribers every morning. As you can see, in the red box you have the jax, which is the Gamma exposure. We will talk more about the JAX and Q models later in the course.

[00:00:41.14] - Speaker 1
There is an easy way to think about Gamma. Gamma is the exposure to historical volatility. When a trader does delta hedging, what they are trying to do is to isolate the delta. If the market moves and becomes volatile, the movement is due to Gamma. So an investor can hedge the delta, isolate the movement of the delta and trade gamma and volatility.

[00:01:00.03] - Speaker 1
So if we have a high Gamma, we have a high Delta and a very fast movement of the underlying price. Risk assets like Bitcoin or stocks like Tesla tend to have higher Gamma. The price of the underlying intraday moves very quickly. A trader who knows how to use options can benefit from that Gamma move. The opposite happens if we have low Gamma.

[00:01:19.06] - Speaker 1
The delta tends to be low and so does the underlying price movement. For example, defensive stocks with lower volatility tend to have a very low Gamma. Here we have a simplified chart of the interaction between Delta, the spot price and Gamma. As we can see, the movement of the spot price causes the delta to change. Gamma is simply the difference between the initial delta and the final delta.

[00:01:40.21] - Speaker 1
In this example, with a $1 movement in the underlying stock, the delta moves from 0 to 0.5. In this case, our gamma is 0.5. One of the concepts that is important to understand is the difference between positive Gamma and negative Gamma. This can also help us understand our Q models better. It is important to understand what it means when the model is in positive Gamma and what it means for our strategies.

[00:02:04.10] - Speaker 1
But it is also necessary to understand how to change strategy when it goes into negative Gamma. In the chart, positive Gamma is the green section above the high volume level while negative Gamma is the red section below the high volume level. Now let's try to understand the concept of long and short Gamma. During the Course, we will then have a section dedicated to RQ models and how you can use them for your strategies. Being long gamma means being long options.

[00:02:28.02] - Speaker 1
For example, buying a call is equivalent to being long gamma. Here we can see a simplified chart on how to do delta hedging in positive gamma. In this case, the investor or market maker is delta neutral. By going short when the market goes up and going long when the market goes down. This can be a very profitable scalping strategy.

[00:02:46.08] - Speaker 1
In this case, a long gamma position pushes the delta to the right side and it is positive for the P L. This happens because the more the underlying rises, the more the delta becomes positive, while when the underlying goes down, the delta becomes negative. On the other hand, being short gamma is the opposite. Being short gamma means being short options. An example is being short a call in negative gamma. To be delta neutral, the market maker goes short when the market falls and goes long when it rises.

[00:03:13.19] - Speaker 1
So the delta when the market rises becomes negative, while when it falls it becomes positive. Here we can see a chart on how to do delta hedging in negative gamma. In this case, to be delta neutral, we sell when the price falls and we buy when it rises. For this reason, the trader must always chase the market on the wrong side. At this point we can already begin to better understand our model.

[00:03:34.08] - Speaker 1
When we are in the green quadrant, we are in positive gamma. This means that the market maker's portfolio is in positive gamma. Every time the market makers hedges pushes the market to the correct side and keeps volatility low. In positive gamma, the investor or trader can benefit by using strategies that profit from low volatility. In the final section, we will then talk about these strategies in more details.

[00:03:55.27] - Speaker 1
When instead we find ourselves in the red quadrant, it means that the market maker's portfolio is in negative gamma. This tends to increase volatility because to stay delta neutral, the market maker shorts when the market goes down and goes long when the market goes up. This increases the speed and direction of price movement. Investors in these cases may use strategies that benefit from high volatility. Now let's try to understand the relationship between delta and gamma.

[00:04:21.07] - Speaker 1
We need to go back to the delta profile. Here we can see the delta profile that we have studied in the previous lessons. What we know by looking at this chart is that the delta tends to be low when we are out of the money starts to rise when we get to add the money and reaches the highest level in the money. At this level the option moves as if we were long underlying. The profile of the gamma is instead Directly related to the delta.

[00:04:43.17] - Speaker 1
Delta is very low. When we are out of the money and the expectations of entering in the money are very far away, There is less uncertainty. The same happens when the option is deep in the money. The uncertainty is gone. The option moves as if we were long.

[00:04:57.12] - Speaker 1
Underlying uncertainty increases when the option gets closer to the money, as in the case of Delta. Also for Gamma, uncertainty is very important. And so we see the peak of Gamma at the money. It declines and collapse when we are deep out of the money or deep in the money. This is a concept to remember and it helps us understand why OPEX expiries are so important.

[00:05:18.25] - Speaker 1
The relationship between Gamma and Theta is very important. Because if there was no theta involved, Going long Gamma would allow you to always gain. Unfortunately, it's not that simple. When we buy a call or a put option, we have to pay a premium. This is the cost of having long gamma exposure.

[00:05:34.14] - Speaker 1
The reason why an option has a premium is because it has a time value. Here we show again the slide on the option value of a call. As you recall, the intrinsic value is the value of the option. After the strike is exceeded. Then we have the time value.

[00:05:49.03] - Speaker 1
So the premium we pay for being long Gamma has a time value. Unfortunately, the time value decreases as time passes. This value is known as time decay. We will talk about theta in the next section, but for now it is important that you understand the relationship with Gamma. As you can see, when we are short Gamma, we are long theta.

[00:06:07.24] - Speaker 1
Being short Gamma means receiving a premium. This means that theta works in our favor. The more time passes, the more our risk decreases. In fact, we are receiving a premium because we are taking the risk that the option goes in the money at expiration. If we are long options, we are long Gamma.

[00:06:23.13] - Speaker 1
In this case, theta is negative for our position. We pay a premium because we want the option to go in the money. The more time passes, the more the value of our option decreases. In this case, the position must enter in the money before the option expires to be profitable. As with the Delta, we know that the further we are from expiration, the flatter the delta profile is.

[00:06:42.28] - Speaker 1
The same also applies to Gamma. As we can see from this chart. The further we are from expiration, the lower the gamma is. As we get closer to expiration at the money option will have a very high gamma as the uncertainty of entering in the money becomes higher. At the same time, the closer we get to expiration, the more the Gamma of out of the money and in the money options decreases.

[00:07:02.25] - Speaker 1
If we look at volatility we can see how it affects gamma. Volatility on the upside tends to be negative for at the money option gammas, while it becomes positive for out of the money and in the money options. Upward volatility increases the time value of the option, especially those that are further away from at the money. So gamma plays a very important role in our strategy. Here we can do a quick recap before moving on to the next Theta at the money options have the higher gamma the closer we get to expiration.

[00:07:29.19] - Speaker 1
Gamma and theta play against each other based on whether we are long or short Gamma. If we change our assumptions on implied volatility at the money Gamma decreases and in the money and out of the money gamma increases. If volatility and theta decreases at the money gamma increases and in the money and out of the money gamma decreases. So Gamma plays a very important role for our strategy. Gamma is an indicator that we use in our models to understand the exposure of market makers.

[00:07:54.29] - Speaker 1
In the next lesson we will talk about the importance of time in our option strategy.