Gamma: Delta's Accelerator for End of Day Options

Hello everyone and welcome back to moomoo. I'm options explorer. In today's [Options ABC], we'll be taking a look at another option Greek: Gamma.

In my previous articles, I discussed Delta, a crucial Option Greek, and the Delta Neutral Strategy. Today, I will be delving into another Option Greek that is closely related to Delta: Gamma. If you are unfamiliar with Delta, feel free to check out our earlier article for more information. However, for those who are ready, let's explore Gamma.

Let's begin with a question: As an option approaches its expiration date, does Gamma generally increase or decrease?

In a previous discussion, we explored the Greek Theta and how it represents time decay, which slowly chips away at an option's premium. However, Gamma provides various possibilities for options with a limited lifespan.

Gamma is the rate of change in an option's Delta per $1 change in the price of the underlying stock. In other words, we can consider Gamma as an indicator of Delta, tracking its changes over time. Keep in mind, Option Greeks are calculated using options pricing models and are theoretical estimates. Greek values are based on the assumption that all other factors remain constant.

To express it in a formula: Gamma = Change in Delta / Change in Stock Price

You may be wondering why it's important to learn about Gamma when we already have Delta as an indicator of changes in the option's premium.

Let's take a look at a hypothetical example to see why.

Let's say Alice buys an at-the-money call option for Stock S with a Delta value of approximately 0.5. This means that if the price of Stock S increases by $100, the option's premium theoretically increases by $50.

However, market conditions can change unexpectedly due to news or policy shifts. If company S announces a long-awaited strategic acquisition, the stock price might leap by $100, and instead of increasing by $50, the option premium could rise by $60 due to Gamma Effect, an additional increase led by Gamma.

Gamma and Delta can be compared to acceleration and speed, respectively. For example, suppose Alice is driving to work at a constant speed of 40 KM/H when she suddenly realizes she needs to arrive at the office half an hour earlier than usual due to schedule changes. To prevent losing pay, Alice accelerates to a speed of 55 KM/H from her previous speed of 40 KM/H. In this hypothetical scenario, Alice's initial speed of 40 KM/H represents Delta, while the change in speed from 40 KM/H to 55 KM/H is similar to the effect of Gamma.

On moomoo, open the options chain and scroll left and right to find Gamma.

In general, a high Gamma value signals a higher level of risk, while a low Gamma value indicates a lower risk level. This is due to the fact that a larger Gamma value implies Delta changes more rapidly with shifts in stock price, resulting in quicker changes in option premium and increased risks. However, a higher risk level also suggests a greater potential for return on investment, so investors must assess their options based on their investment preferences, risk tolerance, and strategies.

Although Gamma is theoretically a positive number, option sellers who hold a short position will see negative Gamma. Therefore, holding a position with a large Gamma is a high-risk practice, especially for option sellers who hold a large negative Gamma position. The biggest risk for option sellers is tail risk. At-the-money options have the highest Gamma value when the expiration date is around the corner, and lower the more time to expiration an option has, all things being equal.

Gamma measures the changes in Delta with changes in stock price. As the expiration date approaches, at-the-money options' Gamma tends to be all its highest because the option price becomes more sensitive to changes in the underlying asset price. In contrast, the Gamma values of in-the-money and out-of-the-money options tend to increase slightly and then decrease as the expiration date approaches. This is because when the expiration date is far away, the primary factor affecting an option's price is its intrinsic value rather than time value. However, as the expiration date approaches, the primary factor affecting an option's price becomes time value, making the option more sensitive to changes in stock price.
In addition, for at-the-money options, the distance between the strike price and the current stock price approximately equals zero. Therefore, at expiration, there is a 50% chance that the option will end up in the money and a 50% chance that it will end up out-of-the-money. At-the-money options are considered to be the balance point between in-the-money and out-of-the-money options, and they are the most sensitive to changes in stock prices. As a result, at-the-money options have the highest Gamma among all options, This means that the option premium of at-the-money options will change more quickly with changes in stock price compared to other options, all other factors being equal.

Think of Gamma as the "acceleration" of Delta, which measures how much an option's premium changes relative to stock price changes. By combining Gamma and Delta, investors can calculate how quickly an options price can potentially move.

A high Gamma value indicates that the option premium may experience rapid changes according to movements in the underlying stock price. Consequently, the potential profit or loss from the option will accumulate quickly. Conversely, if the Gamma value is low, the option premium will change more slowly with respect to fluctuations in the underlying stock price, resulting in slower accumulation of potential profits or losses.

Let's look at a hypothetical example of Alice. Suppose Alice buys an out-of-the-money put option on stock S expiring in three months. Since the option is out-of-the-money and far from expiration, Delta is not very sensitive to changes in stock price, resulting in a relatively low Gamma. Therefore, option's premium will likely change more slowly with respect to fluctuations in the underlying stock price.

However, as the expiration date approaches and the option becomes more sensitive to changes in stock price, its Delta may surge if the stock price decreases, leading to a higher Gamma. At this point, the option's premium will likely change more rapidly with respect to fluctuations in the underlying stock price.

As the expiration date approaches, out-of-the-money options with zero intrinsic value and little time value left become almost worthless. Nevertheless, some investors still trade them in large volumes, and the key to this lies in Gamma.

To illustrate the significance of Gamma, let's assume Alice purchases a call option on stock S with a strike price of $80. On the expiration date, the stock price is $79, and the option is supposed to expire worthless. However, if the stock price surpasses $80 thirty minutes before expiration, the option could increase substantially in value, potentially even doubling. This is because Gamma has a significant impact on options' prices as they near expiration.

When trading End of Day Options, it is vital to remember four rules: setting take-profit orders, establishing stop-loss orders, managing position size, and being prepared to roll down.

Setting take-profit orders should be the first thing to remember when trading End of Day Options because missing the opportunity to close a position at the right time could result in significant losses. For instance, suppose Alice buys a far out-of-the-money call option, and the market suddenly surges. In that case, failure to sell the option at the correct moment could result in Alice losing the chance to close the position and suffering losses. If the option's price falls to $0.01 in the end, Alice will be left with nothing but regret.

Since stop-loss and position management are easier to understand, I'll say a few words on roll down alone. Roll down is an options trading technique where investors close out their current position (thereby realizing any gains or losses) and purchase another option with a lower strike price. For those trading End of Day Options, maximizing Gamma is crucial, and this strategy can be considered among others to help achieve that goal. If the Gamma value of an out-of-the-money option surges and moves it in-the-money, a roll-down can allow traders to potentially profit while managing risk exposure. However, successful roll-downs should be guided by accurate market analysis and risk management. Traders should avoid being too greedy or impatient when trading End of Day Options.

That's all for today! Please feel free to leave a comment if you have any questions or thoughts. Don't forget to follow us to stay up-to-date on all things related to options trading. For more information of options learning, you can click on the image below to follow me immediately!