Get to know the Greeks

Use these tools to enhance your options trading proficiency.

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If you are looking for help trading options, look no further than the Greeks. The term “Greeks” derives from the fact that most are represented by letters of the Greek alphabet.

Greeks are a set of mathematical calculations that are designed to help traders assess risk. They allow for the measurement of the impact that changes in various factors, such as time and volatility, have upon an options contract. While Greeks can be applied generally to other derivatives (securities whose value depends on an underlying asset), they are most well known as a tool used by experienced options traders.

The big one

When it comes to the Greeks, the discussion begins with the most widely used of them all: delta. This is the sensitivity of an options price to the change in the price of the underlying asset. For instance, delta would measure how much the theoretical value of a call option on XYZ Company stock would change, given a change in the value of XYZ stock.

Calculating delta

The formula for delta is computed as the change in the option price, divided by the change in the underlying asset. Assume the cost of an XYZ call is $3, and the underlying stock is trading at $40. If the stock rose to $42, and the cost of the call option increased to $4.50, the delta would be 0.75 [($4.50 – $3) / ($42 – $40)].

It’s not all that important to know how to calculate delta (see the sidebar if you’d like to know how). In fact, many trading programs perform this calculation for you and it can be found in your Fidelity options trading platform for individual contracts.

How might a trader interpret delta? There are actually a few different ways to use it. A 0.75 delta suggests that the price of the option will gain or lose $0.75 on a dollar move for the underlying asset. Let’s look at an example. Suppose that XYZ Company is trading at $40 and the 37.50 call costs $3. If the stock were to increase to $41, the 0.75 delta implies that the theoretical call option price should increase to $3.75. For each dollar move in the underlying asset, the option price would approximately move by the delta.

The delta for a put works similarly, but would be a negative number; as the price of the underlying asset decreases in value, the price of the option increases. Assume XYZ Company is trading at $40, and the 42 put costs $3. If the stock were to decrease from $40 to $39, a delta of 0.75 would imply that the theoretical put option price should increase to $3.75.

Many traders use delta in other ways as well. Some think of delta, in absolute terms, as the probability of an option’s being in the money at expiration. Yet another way to view delta is from a net position on the underlying security. For instance, if a trader holds a call contract with a delta of 0.75, it is equivalent to being long 75 shares of the underlying security. Similarly, holding a put option or shorting a call, with a net delta of –0.75, would be equivalent to being short 75 shares of the underlying security.

Of course, the option value implied by delta is not an exact science. Delta simply implies a theoretical value. Factors will influence the price of an option beyond the price of the underlying asset. Still, delta does serve as a very useful guide, depicting how sensitive to the underlying asset an option might be.

Learning how to use delta as part of your options trading is important. You can learn a lot about how an option trades by observing Greeks, such as delta, for specific contracts over time. Here are some helpful guidelines to get you started:

  • All else being equal, an in-the-money call option’s delta will move toward 1 at expiration, and an in-the-money put option delta will move toward –1 at expiration.
  • Delta may be more sensitive to time to expiration and volatility the further in the money or out of the money the option is.

Greek alphabet soup

In addition to delta, there are a few other Greeks that are widely used by options traders.

Gamma—This Greek is directly related to delta. Whereas delta will change based on a price move in the underlying asset, gamma is the rate of change, or sensitivity, to a price change in the underlying for delta. Basically, gamma measures how well delta describes an option’s sensitivity. Positive gamma accelerates gains and decelerates losses on options contracts; this quality can be found in long calls and long puts. Alternatively, negative gamma decelerates gains and accelerates losses, and is a characteristic of written calls and puts. Gamma’s impact is most noticeable in at-the-money options, and when gamma is large, delta can change rapidly.

Vega—This is a measure of an option price’s sensitivity for a given change in implied volatility. An increase in the implied volatility (i.e., the expected volatility) of an option will increase the value of both call and put options, and falling implied volatility decreases the value of both types of options. Vega can be an extremely useful Greek, particularly when volatility is expected to increase or decrease.

Theta—This Greek measures the effect that time’s decreasing has on an option as it approaches expiration. This is also known as time decay. Theta quantifies how much value is lost on the option due to the passing of time. It is typically negative for purchased calls and puts, and positive for sold calls and puts. Note that it is not advisable for inexperienced traders to trade near expiration, as it can be more complex than when there is more time to expiration.

Rho—There are several other secondary Greeks that are not as widely used as those listed above. Rho is one such Greek. It describes an option’s sensitivity to a change in interest rates. Note that the relationship between interest rates and option value is not significant. Strictly speaking, an increase in interest rates will increase the value of a call option and decrease the value of a put option. If rates were expected to change dramatically, some traders might incorporate Rho into their analysis. In practical terms, interest rates influence option prices very little.

Put Greeks to work

It can take a little time to learn how to interpret Greeks and to determine which ones you think may or may not be helpful. Learning about Greeks, and how changes in market conditions can affect the price of your options, may help you become a better options trader.

Learn more

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Options trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risk. Prior to trading options, you must receive from Fidelity Investments a copy of "Characteristics and Risks of Standardized Options" and call 1-800-343-3548 to be approved for options trading. Supporting documentation for any claims, if appropriate, will be furnished upon request.
Greeks are mathematical calculations used to determine the effect of various factors on options.
Views and opinions expressed may not reflect those of Fidelity Investments. These comments should not be viewed as a recommendation for or against any particular security or trading strategy. Views and opinions are subject to change at any time based on market and other conditions.
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