Complete Guide to Gamma Options

With so many options, it’s easy to get overwhelmed.

We’re only joking (sort of). Options really aren’t as scary as they might appear at first glance – provided that investors do their homework and set off with a well-thought-out plan for how to trade. However, to do that, there are several key elements that have to be rigorously studied – trading options is quite different from standard run-of-the-mill stock trading or buying index funds and ETFs. 🗃

The most important factors to take into consideration when trading options are the Greeks – these metrics measure how sensitive options contracts are to changes in various other factors. There are four of these metrics: Delta, Gamma, Theta, and Vega. Today, we will be covering Gamma.

Gamma is sort of the black sheep of the Greeks – it is the only Greek that is based on another Greek – Delta, to be more precise. But not to worry – only a cursory understanding of Delta is needed for this guide, and the Greeks are so intertwined and interconnected that learning about Delta is certainly a must-do either way.

In this guide, we’ll be covering the basics of Gamma – how it works and how it affects and is affected by changes in other metrics. Once that is done, we’ll move on to slightly more practical orders of business – how it is calculated, what Gamma-based strategies exist, how to apply them, and top it all off with a short quiz.

Although it isn’t the most beginner-friendly approach, all investors who have a baseline of knowledge regarding how to invest should consider trading options. Retail options trading has seen a huge increase since the Covid-19 pandemic – and with stock prices being as expensive as they are, this comes as little surprise. So, let’s see how an enterprising investor can get in on the action.

How Does Options Trading Work? 👷‍♂️

Options are an asset class that is slightly more complex than stocks or ETFs, for example – but there’s nothing to worry about. An options contract is a derivative, meaning that it derives its value from the value of an underlying asset. Therefore, a change in the price of the underlying asset will lead to a change in the price of an option.

So, let’s dive into how options contracts actually operate. Options contracts give investors the right (but not the obligation) to buy or sell a security, at a predetermined price, by a predetermined time.

Although derivatives are often held to be risky, volatile, and more difficult to manage than traditional asset classes, things aren’t really that straightforward. Derivatives, and options in particular, offer a variety of benefits to the average retail investor – chief among them accessibility.

The only expense associated with options is called the options premium. On top of that, buying an options contract for a stock is many times cheaper than actually purchasing the stock itself – while still allowing investors to profit from price changes.

Speaking of profit, how does profiting from options actually work? Let’s use a hypothetical example to illustrate. Athleisure giant Lululemon (NASDAQ:LULU) has an earnings report coming up – and based on past performance, an earnings report will swing the price of the stock in either direction by at least 5%. The stock is, in our example, currently trading at $280 per share.

If other metrics suggest that the earnings report will be positive, instead of purchasing the shares, investors can buy a call option – giving them the right to purchase the stock at $285 per share. Let’s say that 100 options contracts are purchased, each of them priced $3, for a grand total of $300 in expenses.

If the stock price does rise by 5% – in this case, that would be an increase of $14, up to $294, the investor could purchase 100 stocks for a price of $285 each. The difference between the two prices is $294 – $285 = $9, and once we subtract the $3 options premium associated with every contract, the investor is left with a $6 profit from every single contract, for a total of $600.

Gamma in Options Explained 👨‍🏫

As we’ve discussed, being complex financial instruments, options contracts are affected by a wide variety of factors. In essence, everything that has an effect on the underlying asset that any derivative is based on will also have an effect on the options contract.

For reasons of brevity, we won’t be covering everything that affects options prices. Knowing how to research stocks and other asset classes is key to being a successful options trader, but that is not today’s topic.

There are a set of metrics that were tailor-made for options trading – these are referred to as the Greeks: Delta, Gamma, Theta, and Vega. All of the Greeks measure sensitivity to change in some underlying factor. Today, we will be covering Gamma – at first glance, the most complicated of the Greeks.

The Fundamentals of Gamma 📚

Alright – first things first, to understand Gamma, we have to understand another of the Greeks – Delta. The reason behind this is simple – Gamma is a measure of the change in Delta per 1-point move in the price of the underlying asset that the option is based on.

So, what’s the deal with Delta? Well, Delta is a measure of how sensitive an options contract is to changes in the price of the underlying asset. Thankfully, that’s simple and straightforward enough. To be even more precise, Delta measures how the price of an option changes in the case of a $1 change in underlying asset price. To use an example, an option with a delta of +0.45 will become $0.45 more expensive if the asset sees a $1 increase in price.

With that out of the way, we can move on to the star of today’s show – Gamma. We’ll get into how to calculate Gamma later – for now, let’s illustrate how it works with a simple example – and we’ll use the same one we used above.

With a Delta of +0.45, a $1 increase in asset price leads to a $0.45 increase in the price of an option. However, nothing in the world of investing is static – so when that happens, the Delta itself also changes. Let’s say that after the price increase, the value for Delta is +0.61. Because Gamma measures change in Delta, the Gamma of the option is 0.16.

How Does Gamma Behave? 🤓

Being a derivative of Delta, Gamma is primarily used to supplement the information that Delta as a metric provides.  Although how much the price of an options contract will change if the asset price changes is valuable information, Delta is a rather short-term metric – it is subject to change, and on its own, it isn’t useful or applicable for long-term planning.

A useful way of thinking about these two metrics is to consider Delta as the velocity or current speed of an options contract, while Gamma represents acceleration in this metaphor. To get a good overview of how an options contract can perform in anything else other than the short-term, Gamma is essential.

As for the behavior of Gamma, there are a couple of rules that always hold true: the more an options contract goes into the money, the lower the Gamma, approaching zero. In this case, Delta simultaneously approaches the value of 1.

At the same time, the further out of the money an options contract is, Gamma will likewise approach zero. Gamma experiences its highest values for options that are at the money. There is also a third-order derivative based on Gamma called color, also referred to as Gamma decay or the derivative of Gamma with respect to time, which measures the rate of change of Gamma – sort of like a Gamma’s Gamma – but that’s a topic for another time.

Volatility Effects on Gamma 📈

Volatility or Beta (which, oddly enough, isn’t considered one of the Greeks), is a hugely important metric for all approaches to investing. However, it has a rather pronounced and unique relationship with Gamma, so it is worth taking the time to mention it here.

High volatility is beneficial in terms of Gamma – it leads to stable and low Gamma, which, in turn, leads to much more predictable trading. The reason behind this is simple – high volatility means that options contracts that are deeply in the money or out the money have already reached significant time value – meaning that any further increases in time value will be less impactful overall.

On the other hand, low volatility leads to the following: at-the-money options experience high Gamma, while out-of-the-money options experience extremely low Gamma, sometimes even approaching 0. Because the time value of these options is low, any move toward the strike price is significant.

The Basic Uses of Gamma 📗

Now that we’ve covered all the relevant information regarding Gamma, let’s take things in a more practical direction. By now, what Gamma is should be clear – however, this metric is quite versatile and has a part to play in various approaches and strategies for trading options.

Delta Stability 📊

As a derivative of Delta, Gamma can give investors a simple and actionable overview of how stable Delta is. The reason behind this is simple – unlike Delta itself, Gamma is forward-looking and gives investors a clue as to possible future changes.

Using Gamma as a benchmark for Delta stability is incredibly simple – higher Gamma indicates a bigger potential change in Delta – in other words, high gamma equals unstable Delta. Low Gamma, conversely, indicates that potential changes to Delta aren’t as severe, meaning that Delta is stable.

Delta is often used to measure the probability that an options contract will be at the money at the time of expiration. Gamma supplements this by factoring in how stable that probability is.

Long Options Gamma 🛣

Long options contracts, whether they take the form of calls or puts, have positive Gamma – in other words, positive exposure to Gamma. In the simplest of terms, with long options, high Gamma can be a positive sign.

With positive Gamma, an increase in asset price will also lead to an increase in Delta – which can accelerate both gains and losses. So, if it also accelerates losses, how is this a positive? 

The important thing to note is that going long on options can mean purchasing calls or puts – as long as an investor purchases an options contract, they are going long on it. In the case of puts, accelerated losses in stock price can quickly lead to large profits.

In the case of long calls, an increase in asset price makes Delta more positive, while in the case of long puts, an increase in asset price makes Delta less negative (closer to zero). 

If the asset price were to see a decrease in price, however, long calls would see less positive Delta (moving toward 0), while a long put would see more negative Delta (moving toward -1).

Short Options Gamma 🕵️‍♂️

Short options contracts – either puts or calls that are written and sold by investors, have negative Gamma, or negative exposure to Gamma. In other words, in these cases, high Gamma is a negative sign.

There are plenty of popular options trading strategies that have negative Gamma – such as covered calls, iron condors, short puts, and vertical credit spreads. In particular, short uncovered options are very sensitive to Gamma.

In the case of short calls, price increases in the underlying asset lead to Delta that becomes more negative (approaches -1), while in the case of short puts, Delta will become less negative (approaches 0)

Conversely, if asset prices drop, the short calls will see Delta moving toward 0, while short puts will see Delta moving toward +1.

Gamma Hedging 🛠

Gamma hedging is a complex form of risk management that seeks to reduce risk by maintaining a constant Delta value for a portfolio – in many cases, this goal is being Delta-neutral. The purpose of Gamma hedging is to counter the negative effects that sudden and drastic changes in price can have on a position – particularly in the closing days before option expiry.

The calculations behind Gamma hedging are quite complex, and we can’t do them justice here – but we can explain the rationale behind the method. Gamma hedging is done by purchasing additional options contracts, which serve as a counterweight to the investor’s initial position. 

If an investor has a large call position, Gamma hedging is accomplished by buying puts – or alternatively, by purchasing additional calls with different strike prices. Likewise, in the case of a put position, Gamma hedging is accomplished by purchasing calls, or more puts at different strike prices.

Gamma hedging is generally held to be a more in-depth, superior alternative to Delta hedging. However, there is a synthesis of both approaches – Delta-Gamma hedging, which also deserves consideration.

Gamma hedging is essential for advanced options trading, but beginners ought not to worry about it too much – Gamma hedging is well outside of the basics of options trading – this stuff should be learned after mastering multiple strategies for trading options, as well as having a good overview of how to make an options portfolio.

Calculating the Options Gamma 🧮

Before we move on to mathematics and formulas, take a deep breath and don’t panic – there’s no need to do this stuff by hand. The ability to calculate Gamma, as well as the values of other Greeks, has been a mainstay among the leading brokerages for options trading for a long time.

However, although computers and algorithms might take care of the legwork, understanding the mathematics behind Gamma is still important – there is no better way to gain an in-depth understanding of this crucial metric.

The formula for calculating Gamma is as follows: Gamma = (Δ1 – Δ2) / (P1 – P2), where Δ1 is the first value for Delta , Δ2 is the second value for Delta, P1 is the first price of the underlying asset, and P2 is the subsequent price of the underlying asset.

To put things into perspective, let’s use an example – an options contract for an underlying security that is worth $38, with a Delta of 0.6. If the value of the underlying security were to rise to $45, and the new value for Delta were to rise to  0.4, the mathematics would look like this:

= (Δ1 – Δ2) / (P1 – P2)
= (0.6 – 0.4) / ($38 – $45) 
= 0.2 / 0.84 = 0.23.

Although this is a relatively simple formula, it is an approximation. There are other, much more accurate ways to calculate Gamma, but they involve six or seven factors. However, there is no reason to actually do the math by hand – Gamma is a measure that is constantly in flux, so the fact that there are advanced trading tools that do the legwork for investors is a godsend.

Quick Example of Options Gamma 📝

Alright – going off on the example above, let’s go over a couple of more examples, to further clarify. The example above was used to illustrate a simple formula, but going a bit more in-depth can also serve to further explain Gamma as a concept.

Let’s mix it up a little. A long put option has a Gamma of 0.3, a Delta of -0.7, as well as an underlying asset price of $80. Long options have positive Gamma – meaning that an increase in asset price will lead to an increase in Delta.

Suppose that the price of the asset increased to $81 – this would lead to a new Delta value that is = -0.7 + 0.3 = -0.4. If, however, the price of the asset were to decrease to $79, Delta would become more negative – since the change in the underlying asset price is the same, the same change, but reversed, would occur to the value of Delta: -0.18. In that case, the new value for Delta would be -0.7 – 0.3 = -1.0.

When approaching Gamma, traders and investors should always keep in mind how it affects and interacts with other metrics – Delta in particular. Let’s take the time to go over an example of Gamma for short options.

A short put option has negative exposure to Gamma – an increase in asset price leads to a decrease in Gamma. A short call with a Gamma of 0.04 and a Delta of +0.21, with an asset price of $40 will be used for this example.

In the event of the underlying asset’s price rising to $41, the put option would have a new Delta value of 0.21 – 0.04 = -0.17

What Exactly is a Gamma Squeeze? 🤔

In the terminology of investing, a squeeze is a rapid change in stock price that creates a feedback loop. In short, a sharp price move in one direction, something that is always very noticeable, causes investors to sell stocks or change their current positions, as per basic trading psychology. This, in turn, serves to further intensify the price change, which leads to other investors doing the same, creating a self-reinforcing system.

The most publicized squeezes of the last couple of decades are the GME saga and the Volkswagen squeeze. In both of these cases, short squeezes occurred – but another type of squeeze, a Gamma squeeze, is something that is much more important to options traders.

Gamma squeezes are caused by large price swings upwards – which happen when retail investors buy a lot of (mostly) short-term call options. This in itself is a promising sign for a stock, which causes the price of the underlying security to rise. Market makers and other institutional investors, who write options contracts, are on the opposite side of these trades in relation to retail investors.

As more and more call options are purchased, institutional investors are forced to purchase the underlying shares in order to hedge their positions. This serves to further increase the stock price, attracting even more retail investor attention, and the initial rapid price move is only made more rapid and more intense.

It goes without saying that Gamma squeezes, while being quite the opportunity, are always risky. The huge volatility that follows them can last from a couple of days to a couple of weeks, however, Gamma squeezes always end with rapid reversals. Timing is key for those who want to successfully utilize this phenomenon – along with carefully planned out risk management.

Quiz Time: Test Your Knowledge 📜

To cap everything off, here is a simple quiz to help traders get a feel for whether or not they’ve mastered and integrated the contents of this guide. Five questions, with hints provided – but don’t feel any pressure. The Greeks aren’t exactly simple – they are derivative metrics used for financial derivatives, so it is understandable if not everything is crystal clear all at once.

Question 1:
An options contract has a Gamma of 0.32, and a Delta of 0.89. In the event of a $1 price increase, what will be the new value for Delta. Assume that the options contract is a long call.

Hint: Long calls have positive exposure to Gamma – in the case of calls, the value for Gamma is added to Delta.

A: Δ= 0.89 +0.32 =1.21

Question 2:
An options contract has a Gamma of 0.02, and a Delta of -0.48. In the event of a $1 price decrease, what will be the new value for Delta. Assume that the options contract is a short call.

Hint: Short calls have negative exposure to Gamma – in the case of calls, the value for Gamma is added to Delta.

A: Δ= -0.48+0.02 = -0.46

Question 3:
An options contract has a Gamma of 0.28, and a Delta of 0.017. In the event of a $1 price decrease, what will be the new value for Delta. Assume that the options contract is a short put.

Hint: Short puts have negative exposure to Gamma – in the case of puts, the value for Gamma is added to Delta in the case of a price drop.

A: Δ= 0.017+0.28=0.297

Question 4:
An options contract has a Delta of 0.45, After a $1 price move, the new value for Delta is 0.73. What was the Gamma of the options contract?

Hint: Gamma is equal to the difference between the initial value of Delta and its subsequent value after the price move.

A: γ= 0.73 – 0.45 = 0.28

Question 5:
An options contract has a Gamma of 0.13, and a Delta of 0.89. A $1 price change in price occurs. The new Gamma value is 0.15, and another $1 price change occurs. What is the latest value for Delta? Assume that positive Gamma exposure is in effect, and that the options contract is a call.

Hint: To arrive at Delta’s new value, the effect of the first price change has to be calculated vis a vis Delta. After that, the new Gamma value’s effect on the new Delta value has to be calculated.

A:
Δ1= 0.89+0.13 = 1.02
Δ2= 1.02 + 0.14 = 1.17

Conclusion 🏁

Thanks for the attention – and congratulations on making it to the end of the guide. Getting into options trading is a bold move with the potential to be quite lucrative – but it takes time and effort to master this skill.

Metrics, including the other Greeks and Gamma, are essential for options traders – and once they have been mastered, they can be applied in various strategies with various levels of risk. With meticulous study, these abstract metrics can lead investors to a lot of profit – so the sooner one starts, the better.

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