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While I always advocate keeping options trading simple, the “Greeks” are important concepts for beginners. By understanding options Greeks, you will be able to fully appreciate the variables that influence the price of an option. That’s why I wrote this guide to understanding options Greeks for beginners.

### Getting Started with Options Greeks

Delta, Gamma, Theta and Vega, commonly referred to as “The Greeks” are tools for measuring options. The Greeks serve to describe the main characteristics that influence risk, and consequently the price of an option at any given time. By understanding options Greeks, an options trader can make better trading decisions, decrease risk and increase profitable trading opportunities.

The Greeks measure the sensitivity of the price of the option in relation to four 4 different factors:​

• change in the underlying asset’s price​
• shifts in market volatility​
• rate of time decay,​
• and, to a lesser degree, interest rate fluctuations.​

As shown in the table above, the four Greeks that have the most impact on price are Delta, Gamma, Theta and Vega. These Greeks are calculated using a theoretical options pricing model called the Black-Scholes model.

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### Delta

Delta measures the amount an option’s price is expected to change for every \$1 change in the price of the underlying asset.

For example, a Delta of 0.20 means that the option’s price will theoretically move \$0.20 for every \$1 move in the price of the underlying asset. Call options have Delta ranging from zero to one, while put options have Delta ranging from zero to negative one.

At-the-money call options usually have a delta of positive fifty while at-the-money put options’ delta is close to negative fifty.

The Delta of a call option that is trading in-the-money, will get closer to one as expiration approaches.

While a Delta of a put option that’s trading in-the-money near expiration will have a Delta close to negative one.

The Delta of both a call option and a put option will begin moving closer to zero as expiration approaches.

#### Delta As Probability

The option’s Delta is often times used as a gauge to determine the probability that an option will expire in-the-money.

To give you a simple example, if the Delta is .20, that option has roughly a .20% chance of ending up in-the-money at expiration. Another common method of utilizing Delta is to determine how many shares need to be purchased or sold to match the exposure created by the option.

If the Delta is .20, for example, for every dollar that the underlying asset moves either up or down, the option will shift about \$0.20. This information can become very useful in situations when options are being used as a hedge against risk to a stock portfolio.

As an example, let’s say you own \$100.00 shares of ABC stock and you want to protect against downside movement of \$10.00.

You could purchase 2 contracts (each contract = 100 shares) of ABC put options that have a delta of 0.50.

If Delta was 0.25 instead 0.50, you would need 4 contracts instead of 2, to give enough protection in case ABC stock declined \$10.00.

### Gamma

Gamma is the sensitivity of the Delta to changes in price of the underlying asset. The Gamma measures the change in the delta for every \$1 change in the underlying asset.

In other words, Gamma lets you know how much the option’s Delta should change as the price of the underlying asset moves either up or down. In the graph above, you can see how Gamma reacts to three different time frames when the underlying asset is close to the strike price of the option.

Notice that Gamma actually increases as time passes, as long as the option’s strike price is close to being at-the-money. When the asset moves much higher or lower.

There is a strong relationship between Delta and Gamma as the two are dependent on each other.​

For example, let’s assume an option has a Delta of 0.50 and a Gamma of 0.10.

If the underlying asset gained \$1.00 in value, the option would gain \$0.50 in value, and the Delta would now become 0.60.​

As you can see, the Gamma is used as a reference for the change in value of the Delta; similar to how Delta is used to determine the change in the options price.

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### Theta

The Theta value indicates how much the option’s price will diminish per day with all other factors being constant. Simply put, Theta tells you how much the price of an option should decrease as the option nears expiration.

The nearer the expiration date, the higher the theta – and the farther away the expiration date, the lower the theta. Let’s look at a hypothetical example where a call option has a current price of \$3 and a Theta of -0.09.​

The option will lose \$0.09 per day. In two days the option would lose \$0.18 and the call option would now be worth \$2.82.

Note that options lose time value on weekends and holidays.

You should also keep in mind that options derived from stocks and ETF’s that are highly volatile have higher Theta than options derived from stocks that are less volatile.

### Vega

Vega is the measurement of the option’s sensitivity to the change in the volatility of the underlying asset. It represents the amount that the options price shifts in reaction to a 1% change in the volatility of the underlying asset.

To give you a simple example of Vega, assume ABC stock is trading at \$50 in August and the September 55 call option is selling for \$3. For this example, let’s assume the Vega of the option is 0.25 and the underlying volatility is 25%.

If the volatility increases to 26%, the option will increase in price from \$3 to \$3.25. Conversely, if volatility decreases from 25% to 24%, the option would decrease in price from \$3 to \$2.75 As a general rule, Vega inflates when the option is at-the-money and gradually moves lower off as it goes either deeper in the money or further out of the money.​

Furthermore, as you can see from the chart, volatility decreases substantially as the option gets closer to expiration since the probability of a substantial move is reduced greatly with each passing day.

### Recap

• Delta is the expected change in the price of an option when the stock’s price changes by \$1
• Gamma is the expected change in the Delta of an option when the stock’s price changes by \$1
• Theta the expected decrease of an option’s extrinsic value in a 1 day time period
• Vega the expected change in the implied volatility based on specific option price changes

Understanding options Greeks can take much of the guesswork out of the various factors that influence the price of an options contract.

By reviewing the Greeks before purchasing or selling an options contract, you will be in a position to choose the best option from a statistical perspective.