The 5 main Greek options and what they measure

  • The Greeks measure the impact of certain factors on the price of an equity option, namely the price of the underlying option, the decay over time and the implied volatility.
  • Although delta is the change in the price of a stock option based on the change in the price of the underlying stock, it is also used to assess the probability of profitability.
  • The Greeks demonstrate the challenges of options trading, balancing several factors at once.

When trading stocks, making a profit – as well as minimizing risk – is one of the main things investors pay attention to. But for slightly more advanced investors, they might want to try options trading, which comes with additional factors like time decay and


which come with their own complications.

To keep track of these factors, there is something called the Greeks. These measures, represented by various letters of the Greek alphabet, quantify the effect that changes in various factors have on the price of an option.

Understanding options

Options are contracts that give you the right – but not the obligation – to buy or sell a stock at an agreed price, called the strike price, within a specified time, regardless of the price of that stock when you are performing the contract. If your strike price is in a favorable position relative to the current stock price, sometimes referred to as the spot price, then you are “in the money” (ITM). If your strike price and your spot price are equivalent, you are “at par” (ATM). If your strike price is in an unfavorable position, you are “out of the money” (OTM).

There are two types of options you can create: call options and put options. A call option lets you buy the stock at a pre-determined price, which means your strike price must be lower than the spot price to be ITM. A put option allows you to sell a stock at a predetermined price to hedge against the market, meaning you want the spot price to fall below your strike price.

Although options allow you to buy or sell stocks, options themselves are also treated as a security. In fact, this is their primary use.

“Most options are unexercised,” says Randy Frederick, managing director of trading and derivatives at the Schwab Financial Research Center. “Believe it or not, only about 10% of all options are actually exercised. That doesn’t mean it doesn’t mean 90% of them expire, it just means that only about 10% of call options that are purchased are actually used to purchase shares.”

What are the Greeks in options trading?

The market value of an option derives from its ability to acquire stock at a better price. This value is affected by several factors – the price of the underlying stock, the remaining life of the option and volatility are the most important. This is where the Greeks come in. “The Greeks are really a way to quantify the various factors that could affect the price of an option,” Frederick says.

The five main Greek options

There are a myriad of factors that affect the price of an option, but as a retail investor, there are five you should focus on.

Delta: The impact of stock prices

Delta measures how much the price of an option will change if the price of its underlying stock changes by one dollar. The delta of an option will be between -1.0 and 1.0 – and call options have positive deltas while put options have negative deltas.

For example, the price of a call option with a delta of 0.5 will increase by $0.50 for every $1 the stock increases. Since put options have an inverse relationship with the price of its underlying stock, a put option with a delta of -0.5 would rise in price for every dollar that the price of its underlying stock falls.

Delta can also be used to indicate the probability that an option will expire ITM, meaning you will make a profit if you exercise the option. Although an option with a higher delta is more likely to expire ITM, it is also more expensive.

The delta of an ATM option usually sits at a value of 0.5, which means there is an equal chance that an option will expire ITM or OTM. Indeed, “if nothing happens in a company on a given day, [the stock price] could go up a dollar or it could go down a dollar. It’s about 50-50,” Frederick said.

But delta usually fluctuates over the life of an option because the probability of an option ending in ITM changes over its life.

Let’s say that the price of the underlying stock of a call option increases by $1 relative to the option’s strike price. The option is now a dollar in the money, which means it is even further from being out of the money. For every dollar the stock price rises, it becomes that much less likely that the stock will fall enough to fall out of the money.

An option’s delta also changes depending on the distance from the option’s expiration date. If a stock is in-the-money near its expiration date, chances are that option will stay in-the-money, which means its delta will increase. Alternatively, if a stock is OTM close to its expiration date, it is unlikely to make money in that short period of time.

Gamma: the delta change

Gamma falls into a category known as second-order derivative Greek, sometimes simply called second-order Greek. The Greeks who fall into this category do not measure direct changes in the price of an option. Instead, it measures changes among first-order Greeks. Frederick compares this to the difference between velocity and acceleration in high school physics.

In this case, gamma measures the change in delta, which fluctuates over the life of an option. It will go from 0 to 1.0. Gamma is highest when an option is ATM and when the option is nearing its expiration date.

Gamma can also be thought of as a measure of an option’s stability. A high gamma means that the delta changes frequently, suggesting volatility, which can amplify gains or losses. This may be unappealing to investors looking for something stable.

Theta: the impact of time decay

Options have a limited lifespan – most have a maximum lifespan of one year. An expiration date limits how long an option must appreciate. As the option gets closer to expiration, its upside potential decreases, which lowers the price of the option. The rate at which the price falls due to time decay is called theta.

Theta is measured in a dollar amount that the price of an option drops per day. It’s always negative because time only moves in one direction. The rate of decay will begin to accelerate as the contract expiration date approaches, at which time the contract expires worthless.

Vega: the impact of implied volatility

Vega measures the impact of the implied or expected volatility of the underlying stock on the price of a stock option. The price of an option benefits from higher implied volatility because it increases the likelihood that at some point the stock price will land ITM. “[Vega] tells you how much a 1% change in that stock’s expected volatility impacts an option’s price,” Frederick says.

Vega is expressed as a dollar amount per percentage point that implied volatility moves. If an option has a vega of 0.2 and the implied volatility of the underlying stock increases by 2%, the option price will increase by $0.40. An increase in vega will increase the price of put and call options.

Frederick says some traders will take advantage of the increased implied volatility during earnings season when companies report earnings for the year. “If a company says, ‘Hey, we’re going to announce earnings on Thursday of this week,’ options on that particular stock will get very expensive,” Frederick said.

Rho: The impact of interest rates

Rho measures the change in the price of an option if interest rates change by 1%. An increase in interest rates will cause call option prices to rise and put option prices to fall. It is calculated similarly to vega as the value added or subtracted from the option price for each 1% change in interest rates.

Rho is situationally important. They are particularly important in times of high interest rates. They also have a greater impact on long-term stock options (LEAPS), which expire between one and three years after inception and during periods of high interest rates.

Minor Greeks

As a novice options trader, there are some Greeks that are more important to understand than others. The delta is the most important, with its dual function as the rate of price change and a measure of the probability of profit. Theta is a close second, followed by vega. Rho is only applicable in certain scenarios.

Second derivatives such as gamma are one degree of separation away from the price of an option, which makes them a little more complicated to understand and less important. “People new to options really don’t need to understand gamma, they can just put it away,” Frederick says.

Although the aforementioned factors are the most important, they are not the only Greeks in the Pantheon. There are various other Greeks that quantify aspects of an option, such as vomma, a second-order derivative that measures the change of vega. Epsilon measures the impact of a change in dividend yields on stock options.

Part of the reason options trading can be so difficult, especially for first-time investors, is that you’re considering multiple factors at the same time. Even if the price of the underlying stock rises, the option price may not rise because volatility has fallen or the stock price has risen too late and any profit you have made has been canceled by the degradation of the weather.

Comments are closed.