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# Option Greeks Cheat Sheet – Ultimate Guide to Options Math

Options

Options Greek Cheat Sheet is the best guide for options traders. How so? Because it serves as a quick reference guide for options traders to sum everything up.

Do you want to know about Stock Options Greeks and Options Greek Cheat Sheets? Then you are on the right platform at the right time. In this article, we are going to explain in detail the Options Greeks traders use. Additionally, our Options Greek Cheat Sheet is also going to help you beyond your imagination. Let’s begin!

## Options Greeks definition

Options Greeks are dimensions that help options traders gauge the risk associated with an option contract. Additionally, they also enable traders to measure the sensitivity of options to different variables that contribute to those risks. Greek letters Delta, Gamma, Theta, and Vega represent those variables.

## Explanation of Options Greeks

The Greeks refer to different risk dimensions that you face during options trading. The term “Greeks” collectively represents those risk dimensions. Greek letters Delta, Gamma, Theta, and Vega represent those variables.

The Greeks are very helpful tools in options trading. They help options traders in risk management and empower them to make informed trading decisions. In other words, you can easily decide when to buy, when to sell, and what to trade by using Options Greeks.

As you know, there are certain variables such as interest rate changes, price fluctuations, and the passage of time that significantly affect options prices. AND Options Greeks are tools that can also help you gauge options’ sensitivity to those variables.

Furthermore, there are primary and minor Greeks. Primary Greeks include Delta, Gamma, Theta, and Vega. These are commonly used by traders for risk management and are very important. Whereas, traders don’t use minor Greeks as often and are less important.

## Options Greeks

### 1. Delta

Delta is the first risk dimension in Options Greeks. It represents the sensitivity of the price of an option to the price change of the underlying asset. Let’s suppose that the underlying security is the stock. So, the formula of Delta of a stock option is;

Delta of a stock option = Change in price of stock option ÷ Change in price of a stock

#### The effects of stock price change on an option’s price

The following are the key rules you should keep in mind.

• Call options – Delta is a positive value for call options. It means the price of the stock option will increase with increasing stock price.
• Put options – Delta is a negative value for put options. It means the price of the stock option will increase with decreasing stock price.

#### Examples to understand the effects of stock price change on a call option’s price

Let’s first try to understand what happens to a call option’s price when the stock price fluctuates. We are going to consider a scenario. The scenario is;

• Current price of the underlying stock = \$100
• Call option premium = \$15
• Delta of the call option = 25% or 0.25

Now, let’s consider different cases for a better understanding of what happens to a call option’s price when the stock price changes.

Case 1: Stock price increases by \$1 and gets \$101

As Delta is a positive value for call options, the price of the stock option will increase with increasing stock price. That means the call option premium will rise by 25% × (\$101 – \$100) = \$0.25 and reach (\$15 + \$0.25) \$15.25.

Case 2: Stock price increases by \$5 and gets \$105

Now, the call option premium will rise by 25% × (\$105 – \$100) = \$1.25 and reach (\$15 + \$1.25) \$16.25.

Case 3: Stock price declines by \$1 and gets \$99

The call option premium will decrease by 25% × (\$100 – \$99) = \$0.25 and reach (\$15 – \$0.25) \$14.75.

Case 4: Stock price declines by \$5 and gets \$95

The call option premium will decrease by 25% × (\$100 – \$95) = \$1.25 and reaches to (\$15 – \$1.25) \$13.75.

#### Examples to understand the effects of stock price change on a put option’s price

Now is the turn to understand what happens to a put option’s price when the stock price fluctuates. Again, we are going to consider a scenario. The scenario is;

• Current price of the underlying stock = \$100
• Put option premium = \$5
• Delta of the call option = 10% or 0.10

Now, let’s consider different cases for a better understanding of what happens to a put option’s price when the stock price changes.

Case 1: Stock price increases by \$1 and gets \$101

As Delta is a negative value for put options, the price of the stock option will increase with decreasing stock price. That means the put option premium will fall by 10% × (\$101 – \$100) = \$0.10 and reach (\$5 – \$0.10) \$4.90.

Case 2: Stock price increases by \$5 and gets \$105

Now, the put option premium will fall by 10% × (\$105 – \$100) = \$0.50 and reaches to (\$5 – \$0.50) \$4.5.

Case 3: Stock price declines by \$1 and gets \$99

The put option premium will increase by 10% × (\$100 – \$99) = \$0.10 and reach (\$5 + \$0.10) \$5.10.

Case 4: Stock price declines by \$5 and gets \$95

The put option premium will decrease by 10% × (\$100 – \$95) = \$0.5 and reach (\$5 + \$0.50) \$5.50.

### 2. Gamma

Gamma is the second dimension and is related to Delta. It represents the rate of change of Delta relative to the price change of the underlying asset. Options traders use this measure to forecast changes in the Delta of an option. It helps them determine the stability of Delta. Moreover, Gamma is always positive and its value remains within the range of 0 to 1.0.

Let’s try to understand the Gamma dimension through an example. Suppose that 0.10 is the Gamma value of an option. So, the Delta will increase or decrease by 0.10 if the price of the underlying asset increases or decreases by \$1.

Furthermore, the higher Gamma value indicates a more unstable Delta as the price of the underlying security changes. It is also important to note that Gamma will always be high for at-the-money or closer to expiration options contracts. For example, a Gamma value of 0.10 indicates a stable Delta. Conversely, a Gamma value of 0.80 or 0.90 indicates a highly unstable Delta.

### 3. Theta

Theta is the third dimension of the Options Greeks. It represents the rate of an option’s time decay. In simplest words, Theta is a measure that determines how much an option’s value changes with each passing day as the expiration date approaches.

As a general rule, options tend to lose value with each passing day and the expiration date gets near. Therefore, Theta is a negative value. Furthermore, the Theta value tends to gradually increase because the time to make a profit from an options contract decreases.

Moreover, Theta is a very important measure for options traders. Why so? Because it measures time decay and time decay is an important aspect in options traders. It is because time decay is good for sellers while bad for buyers. Sellers’ odds of making a profit increase with the passage of time because time decreases for taking action. Conversely, it is bad for buyers because the passage of time decreases their chances of making a profit.

### 4. Vega

Vega is the fourth and also an important dimension in the Options Greeks. It represents the sensitivity of an option to volatility. In simple terms, it helps traders determine how much the price of an option changes with a 1% change in the volatility of the underlying asset. An increase in Vega value is good for both call and put options as it increases their price. Conversely, a decrease in Vega value decreases the value of both call and put options.

As volatility is among defining factors that affect the price of options, Vega is an essential measure. That said, options traders must keep Vega in mind. As a general rule, they should seek options that are less sensitive to volatility.

## Options Greek Cheat Sheet

After understanding Options Greeks, it is time to seek help from the Options Greek Cheat Sheet. Options Greek Cheat Sheet helps you as a quick reference guide to sum everything up pretty quickly. Thus, you can double-check your trading decisions as well as save a lot of time by using the Options Greek Cheat Sheet.

### Options Greek Cheat Sheet for Delta of a stock option

• Delta for call options is positive
• Far OTM Calls have the lowest Delta value while Deep In the Money (ITM) Calls have the highest Delta value
• Delta for put options is negative
• Far Out of the Money (OTM) Puts have the lowest Delta value while Deep ITM Put have the highest Delta value
• Delta increases as expiration approaches

### Options Greek Cheat Sheet for Gamma of a stock option

• Gamma for long options is positive
• Gamma increases when volatility decreases and vice versa
• Gamma for options increases as expiration approaches
• Gamma reduces when the strike price moves away from the current stock price in either direction

### Options Greek Cheat Sheet for Theta of a stock option

• Theta is negative for long options
• Theta is positive for short options
• Theta values are always high for ATM options and reduce as prices move in either direction
• Theta is highest as expiration approaches

### Options Greek Cheat Sheet for Vega of a stock option

• Vega is positive for long options and vice versa
• Vega value is high for ATM stock options and reduce when the strike prices move away from the current stock price in either direction
• Vega for options decreases as expiration approaches

#### Russell Crane

Russell is an Algorithmic & Technical Analyst Trader @ PatternsWizard.
His passion is to share his knowledge about TA, patterns & more. Why hope for your trading to work when you can precisely know the performance stat of every pattern?

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