Options traders often invoke the "Greeks." What are they, and more importantly, what can they do for you?
In short, the Greeks refer to a set of calculations you can use to measure different factors that might affect the price of an options contract. With that information, you can make more informed decisions about which options to trade, and when to trade them.
They are:
- Delta, which can help you gauge the likelihood an option will expire in-the-money (ITM), meaning its strike price is below (for calls) or above (for puts) the underlying security's market price.
- Gamma, which can help you estimate how much the Delta might change if the stock price changes.
- Theta, which can help you measure how much value an option might lose each day as it approaches expiration.
- Vega, which can help you understand how sensitive an option might be to large price swings in the underlying stock.
- Rho, which can help you simulate the effect of interest rate changes on an option.
Now that you've been introduced, we can explore these calculations in more detail.
Delta
Delta measures how much an option's price can be expected to move for every $1 change in the price of the underlying security or index. For example, a Delta of 0.40 means the option's price will theoretically move $0.40 for every $1 change in the price of the underlying stock or index. As you might guess, this means the higher the Delta, the bigger the price change.
Traders often use Delta to predict whether a given option will expire ITM. So, a Delta of 0.40 is taken to mean that at that moment in time, the option has about a 40% chance of being ITM at expiration. This doesn't mean higher-Delta options are always profitable. After all, if you paid a large premium for an option that expires ITM, you might not make any money.
You can also think of Delta as the number of shares of the underlying stock the option behaves like. So, a Delta of 0.40 suggests that given a $1 move in the underlying stock, the option will likely gain or lose about the same amount of money as 40 shares of the stock.
Call options
- Call options have a positive Delta that can range from 0.00 to 1.00.
- At-the-money options usually have a Delta near 0.50.
- The Delta will increase (and approach 1.00) as the option gets deeper ITM.
- The Delta of ITM call options will get closer to 1.00 as expiration approaches.
- The Delta of out-of-the-money call options will get closer to 0.00 as expiration approaches.
Put options
- Put options have a negative Delta that can range from 0.00 to –1.00.
- At-the-money options usually have a Delta near –0.50.
- The Delta will decrease (and approach –1.00) as the option gets deeper ITM.
- The Delta of ITM put options will get closer to –1.00 as expiration approaches.
- The Delta of out-of-the-money put options will get closer to 0.00 as expiration approaches.
Gamma
Where Delta is a snapshot in time, Gamma measures the rate of change in an option's Delta over time. If you remember high school physics class, you can think of Delta as speed and Gamma as acceleration. In practice, Gamma is the rate of change in an option's Delta per $1 change in the price of the underlying stock.
In the example above, we imagined an option with a Delta of .40. If the underlying stock moves $1 and the option moves $.40 along with it, the option's Delta is no longer 0.40. Why? This $1 move would mean the call option is now even deeper ITM, and so its Delta should move even closer to 1.00. So, let's assume that as a result the Delta is now 0.55. The change in Delta from 0.40 to 0.55 is 0.15—this is the option's Gamma.
Because Delta can't exceed 1.00, Gamma decreases as an option gets further ITM and Delta approaches 1.00. After all, there's less room for acceleration as you approach top speed.
Theta
Theta tells you how much the price of an option should decrease each day as the option nears expiration, if all other factors remain the same. This kind of price erosion over time is known as time decay.
Time-value erosion is not linear, meaning the price erosion of at-the-money (ATM), just slightly out-of-the-money, and ITM options generally increases as expiration approaches, while that of far out-of-the-money (OOTM) options generally decreases as expiration approaches.
Time-value erosion
Source: Schwab Center for Financial Research
Vega
Vega measures the rate of change in an option's price per one-percentage-point change in the implied volatility of the underlying stock. (There's more on implied volatility below.) While Vega is not a real Greek letter, it is intended to tell you how much an option's price should move when the volatility of the underlying security or index increases or decreases.
More about Vega:
- Volatility is one of the most important factors affecting the value of options.
- A drop in Vega will typically cause both calls and puts to lose value.
- An increase in Vega will typically cause both calls and puts to gain value.
Neglecting Vega can cause you to potentially overpay when buying options. All other factors being equal, when determining strategy, consider buying options when Vega is below "normal" levels and selling options when Vega is above "normal" levels. One way to determine this is to compare the historical volatility to the implied volatility. Chart studies for both values are available on StreetSmart Edge®.
Rho
Rho measures the expected change in an option's price per one-percentage-point change in interest rates. It tells you how much the price of an option should rise or fall if the risk-free interest rate (U.S. Treasury-bills)* increases or decreases.
More about Rho:
- As interest rates increase, the value of call options will generally increase.
- As interest rates increase, the value of put options will usually decrease.
- For these reasons, call options have positive Rho and put options have negative Rho.
Consider a hypothetical stock that's trading exactly at its strike price. If the stock is trading at $25, the 25 calls and the 25 puts would both be exactly at the money. You might see the calls trading at, say, $0.60, while the puts could be trading at $0.50. When interest rates are low, the price difference between puts and calls will be relatively small. If interest rates increase, the gap will get wider—calls will become more expensive and puts will become less so.
Rho is generally not a huge factor in the price of an option, but should be considered if prevailing interest rates are expected to change, such as just before a Federal Open Market Committee (FOMC) meeting.
Long-Term Equity AnticiPation Securities® (LEAPS®) options are far more sensitive to changes in interest rates than are shorter-term options.
Implied volatility: like a Greek
Though not actually a Greek, implied volatility is closely related. Implied volatility is a forecast of how volatile an underlying stock is expected to be in the future—but it's strictly theoretical. While it's possible to forecast a stock's future moves by looking at its historical volatility, among other factors, the implied volatility reflected in the price of an option is an inference based on other factors, too, such as upcoming earnings reports, merger and acquisition rumors, pending product launches, etc.
Key points to remember:
- Figuring out exactly how volatile a stock will be at any given time is difficult, but looking at implied volatility can give you a sense of what assumptions market makers are using to determine their quoted bid and ask prices. As such, implied volatility can be a helpful proxy in gauging the market.
- Higher-than-normal implied volatilities are usually more favorable for options sellers, while lower-than-normal implied volatilities are more favorable for option buyers, because volatility often reverts back to its mean over time.
- Implied volatility is often provided on options trading platforms because it is typically more useful for traders to know how volatile a market maker thinks a stock will be than to try to estimate it themselves.
- Implied volatility is usually not consistent for all options of a particular security or index and will generally be lowest for at-the-money and near-the-money options.
StreetSmart Edge® has charting studies for historical volatility and implied volatility. By comparing the underlying stock's implied volatility to the historical volatility, you can sometimes get a good sense of whether an option is priced higher or lower than normal.
Putting Greeks to work
StreetSmart Edge allows you to view streaming Greeks in the options chain of the trading window and in your watch lists. Here is what it looks like.
Streaming Greeks in the trading window
Source: StreetSmart Edge
Streaming Greeks in a watch list
Source: StreetSmart Edge
You can arrange the columns to display in any order you like. And, as shown below, you can choose between three of the most widely used pricing models. In addition, the dividend yield and 90-day T-bill interest rate are already filled in. You can use these values or specify your own.
Choose from three widely used pricing models
Source: StreetSmart Edge
*The values of "risk-free" U.S. Treasury bills fluctuate due to changing interest rates or other market conditions and investors may experience losses with these instruments.
Upbeat music plays throughout.
Narrator: If you dig deep down into your high school memories, you can probably uncover some facts about Greek mythology.
Like Zeus, the ruler of Olympus, and all the gods. Hades, lord of the underworld. And…all those other guys in between.
Well, those memories aren't so clear anymore. But don't worry. Today, we'll focus on a different group of greeks—the options greeks.
Like the ancient gods, these greeks oversee certain domains, including price, time, and implied volatility. The greeks are an important part of options trading, as they tell you how changes in certain factors may impact the price of an option. So, let's get to know them.
We'll start with delta. Like Zeus, delta is the ruler over all the other options greeks because it often has the biggest impact on the value of an option.
Delta's domain is price—it identifies how much the options premium may change if the underlying price changes $1.
This means that a call option with a delta of .40 would be expected to increase by $0.40 if the underlying rose $1.
Delta has another important use as well. Some traders might use it to estimate the probability of an option expiring in the money. For example, an option with a delta of .40 can also be interpreted as having a 40% chance of expiring in the money. The lower the delta, the lower the odds that the option will expire in the money.
One important thing to note about delta is that it doesn't have a constant rate of change. It grows as an option moves further in the money and shrinks as it moves further out of the money. To understand how this works, let's look at the next greek: gamma.
Gamma is delta's Hermes, his right-hand man in the price domain. Gamma measures delta's expected rate of change.
If an option has a delta of .40 and a gamma of .05, the premium would be expected to change $0.40 with the first $1 move in the underlying. Then, to figure out the impact of the next dollar move, simply add delta and gamma together to find the new delta: .45.
Let's move on to theta, the greek of time decay. Theta estimates how much value slips away from an option with each passing day.
If an option has a theta of negative .04, it would be expected to lose $0.04 of value every day.
Remember, time decay works against buyers and for sellers.
Finally, there's vega, whose domain is implied volatility. Vega estimates how much the premium may change with each one percentage point change in implied volatility.
There are a lot of factors that could cause a spike in implied volatility: earnings announcements, political conditions, and even weather. Depending on the strategy you choose, a spike in volatility could be a blessing, a curse, or have a very small impact. And the further out an options expiration is, the higher its vega will be. In other words, options with a longer expiration may react more to a change in volatility.
If an option has a vega of .03 and implied volatility decreases one percentage point, the premium would be expected to drop $0.03.
Now, let's talk about the little brother of the options greeks: rho. Rho identifies how much an options premium may move if interest rates change. Because rates change slowly, they have a smaller impact on options trading.
Like all little siblings, though, rho is often left out of discussions about the greeks. Nonetheless, rho is still part of the family, so he's still worth mentioning here. Now, let's pull our greek council together and look at how they can be used to analyze the sensitivities of a single option. To set the stage, let's say your options premium is $1.30. And your option has a delta of .35, gamma of .06, theta of .02, and vega of .07.
Today, price moves from $45 to $46, and the premium increases $0.35 to $1.65. Because a day has passed, the premium decreases $0.02 due to theta.
Tomorrow, price moves from $46 to $47. The premium increases $0.41 to $2.04; this is delta plus gamma.
Also, another day gone by, means another day of time decay, and another $0.02 down the drain.
Implied volatility rises one percentage point, increasing the premium by $0.07 to $2.09.
Putting all these factors together shows how a relatively small change in the underlying can lead to a pretty significant change in the options premium.
The options greeks are a helpful crew to know. They help you understand the impact various factors can have on options trades. You'll get to know them very well as you continue your options education.
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