Get to Know the Options Greeks

Delta measures how much the price of an option 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 price of the option will theoretically move $0.40 if the price of the underlying stock or index changes $1. 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, meaning its strike price is below (for calls) or above (for puts) the underlying security's market price. 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 because option buyers have to contest with time decay, which we'll discuss more during the theta section.

Here are the greeks for call options, which give the buyer the right to purchase the underlying at a set price prior to the designated expiration date:

• A positive delta can range from 0.00 to 1.00.
• At-the-money (ATM) options usually have a delta near 0.50.
• Delta should increase (and approach 1.00) as the option gets deeper ITM.
• Delta of ITM call options will likely get closer to 1.00 as expiration approaches.
• Delta of out-of-the-money (OTM) call options should typically get closer to 0.00 as expiration approaches.

Here are the greeks for put options, which give the buyer the right to sell the underlying at a set price prior to the designated expiration date:

• A negative delta can range from 0.00 to –1.00.
• ATM options usually have a delta near –0.50.
• Delta should decrease (and approach –1.00) as the option gets deeper ITM.
• Delta of ITM put options will likely get closer to –1.00 as expiration approaches.
• Delta of OTM put options should typically get closer to 0.00 as expiration approaches.

Where delta is a snapshot in time, gamma measures the rate of change in the delta of an option over time. If you remember high school physics class, think of delta as speed and gamma as acceleration. In practice, gamma is the rate of change in the delta of an option per $1 change in the price of the underlying stock.

In the example above, we used an option with a delta of 0.40. If the underlying stock moves $1 and the option moves $0.40 along with it, the delta is no longer 0.40. Why? This $1 move would mean the call option is now even deeper ITM, so its delta should move even closer to 1.00. Let's assume that as a result delta is now 0.55. The change in delta from 0.40 to 0.55 is 0.15—this is the gamma of the options contract.

Because delta can't exceed 1.00, gamma decreases as an option moves further ITM and delta approaches 1.00. After all, there's less room for acceleration as you approach top speed.

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.

For long calls and puts, theta is always negative, which indicates that the option loses value as time passes. For example, an option with a theta of –0.02 would theoretically lose $0.02 of value every day (including weekends). Like the other greeks, theta doesn't stay the same—it tends to increase closer to expiration, which means options lose value faster as expiration approaches.

Vega measures the rate of change in price of the option 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 the price of the option should move when the volatility of the underlying security or index increases or decreases.

• 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 your 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 the thinkorswim^® platform.

Rho measures the expected change in the price of an option 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.

• 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 ATM. 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 cheaper.

Rho is generally not a huge factor in the price of an option, but it 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 shorter-term options.

Implied volatility has a couple of uses beyond vega. Some traders use it to forecast how volatile an underlying stock is expected to be in the future—but it's strictly theoretical. Implied volatility reflected in the price of an option is an inference based on option market participants' expectations of future price moves. Expectations can change depending on upcoming earnings reports, merger and acquisition rumors, pending product launches, etc.

Figuring out exactly how volatile a stock will be at any given time is difficult, but looking at implied volatility can be a helpful tool in gauging market expectations. Higher-than-normal volatilities warn the underlying security may experience larger-than-expected moves. 

However, higher-than-normal implied volatilities are usually more favorable for option sellers, while lower-than-normal implied volatilities are more favorable for option buyers because volatility often reverts back to its average level over time.

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.

The thinkorswim platform allows you to view streaming greeks on the Trade tab. Here's what it looks like.

Another preset layout gives you the implied volatility, probability of expiring OTM, and delta. This layout could benefit option sellers because they can see areas of high implied volatility and identify strikes that may have a higher likelihood of expiring OTM with the thinkorswim proprietary calculator as well as the delta. Selling expensive premiums with a low likelihood of being exercised could be a potential strategy in a trader's playbook.