Investing > Trader’s Guide to Options Greeks

Trader’s Guide to Options Greeks

We can’t know if the price of an option is right without consulting the Greeks first.

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Updated January 06, 2023

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Do you ever wonder how they come up with prices for options?

Contrary to popular belief, option writers don’t use a Ouija board with numbers. Instead, they use math! 📙

To be specific, options are valued based on a few measurements: Delta, gamma, theta, and vega. We call these four Greeks because they are letters from the Greek alphabet. Well, except vega—that’s not a Greek letter and someone just made it up (it does sound kind of cool, though).

But regardless of etymology, these four measurements tell us how an option’s price will react to changes in the price of the underlying stock, changes in volatility, and how quickly its value will decline over time. This information is very important because it gives an idea about whether an option is worth the price—and when volatility is so high that it can turn the markets upside down overnight, prudent and cost-effective trading is a necessity.

All in all, the Greeks are the central part of every seasoned options trader’s toolkit because they are key for determining whether a trader should buy or sell an option (which is kind of what options traders often do for a living). In this article, we will discuss what each of the major Greeks does, how to use them, and how they are calculated. 

What you’ll learn
  • How Options Contracts Work
  • What Are Option Greeks?
  • Option’s Delta
  • Option’s Gamma
  • Option’s Vega
  • Option’s Theta
  • An Explanation of Minor Greeks
  • Conclusion
  • FAQs
  • Get Started with a Stock Broker

A Breakdown of How Options Contracts Work

Buying a lot of stocks is expensive, so traders created options trading—purchasing an options contract gives its owner the ability to either buy or sell 100 shares of a stock, and a predetermined point in time adequately called an option’s expiry date. An option’s price is called a premium and it is always dramatically lower than the price of 100 shares.

Using options, investors can trade shares in large quantities without too much capital and without exposing themselves to huge risks. Namely, the worst possible scenario of an options trade is losing money on the premium—and this is one of the reasons why options trading is always alive, even in very pessimistic and volatile markets.

Premiums are based on a few risk factors, some of which are based on 4 coefficients we call “Greeks”; they bear the names of letters from the Greek alphabet. These are gamma, delta, theta, and vega.

Volatility of an Option 📊

One of the chief factors that determine the price of an options contract is implied volatility. Essentially, volatility measurements indicate how reactive an opinion’s premium will be to the changes in the underlying stock—higher volatility means that the option’s value will have greater upswings and downswings, whereas low-volatility options have smaller price fluctuations.

Many things can impact volatility: Market sentiment, interest rates, commodity prices, and even inflation can drive volatility through the roof like it did in Turkey in 2022 when the lira had its debacle. A fearful market also usually causes heightened volatility. All these factors can impact the underlying stock, and therefore, the options contract itself.

A high-volatility option for a stock that is on a strong downward trend will be cheaper because it is expected to lose big. On the other hand, volatility can be good for a bullish stock, so volatility impacts an option’s premium depending on the context.

Gamma and theta are the Greeks that are based on implied volatility. Namely, gamma measures how much an option’s value will be changed by a 1% move in the underlying’s price, and theta measures how a $1 change in underlying’s price will impact the option’s premium.

An Option’s Profitability 💰

The option’s potential profitability depends on two things—the option’s premium, and its strike price. For example, if a stock is trading at $60 and we have a call option with a strike price of $55 that is very close to its expiry date, we can sell the option at a profit.

Simply, if we wait for the expiry date, that would give us the ability to buy shares for $5 less than their current price and sell them immediately for a profit. That’s why we can sell the option itself at a profit—whoever buys it will have a very high chance of profiting themselves. 

If we make a $5 profit off of each share and we have 100 shares, that means that our total profit here would be $500. But before all that, we paid the option’s premium—the profits we make have to be greater than the premium for the trade to be profitable. This is why an option’s profitability (and thus value) is determined by the strike price and the premium.

What Affects Options Prices? 🤔

Most of all, the prices of options are affected by the price movements in their underlying assets. For instance, when the FED announced that it will stop buying bonds and that it will increase interest rates in 2022, that drove options traders to bet against corporate bonds, and that caused a spike in the price of such options contracts.

Another major factor is time: The closer an option is to its expiry date, the more unlikely it is to change in value, and thus it loses potential profitability—this is factored into the price.

But before anything, the strike price is the most important factor—the difference between the strike price and the underlying’s price is all that matters in the end, so options contracts with unrealistic strike prices are often much cheaper. The last piece of the puzzle is volatility, and as we discussed earlier, volatile assets are necessarily good or bad but they tend to have more aggressive price movements.

What Are Option Greeks? 📚

The price of a stock can be impacted by countless factors, and the best traders know how to look at the most important ones—good analysis equals good predictions. However, being derivatives, options contracts have even more price factors that are options-specific.

For instance, an options contract’s premium will be based on how high the strike price is, how far away the expiry date is, and so on. This makes options a bit more complicated than stocks, but luckily, we can boil all that added complexity down to four letters from the Greek alphabet: delta, gamma, vega, and theta.

They may not have beards, but like the famous Greek thinkers of old, these four letters measure things:

  • Delta: Measures how much the price of an option will change if the underlying asset’s price changes by $1.
  • Gamma: Measures how much an option’s delta will change if the underlying asset’s price changes by 1 point ($1).
  • Vega: Measures how much the price of an option will change if its implied volatility changes by 1 point.
  • Theta: Measures the rate at which an option loses value due to its expiry date approaching.

As we can see, these four are made to work as a team, and together, they measure the risk that an options contract carries independently of the underlying stock. In other words, these four Greeks are not tasked to analyze a stock, but to measure how risky or profitable an options contract for that stock is. Let’s take a closer look at all four.

🧠 Helpful tip: Most of the top platforms for options trading are completely free and provide all the Greeks and other data on all listed options, which is why options traders prefer these specialized services.

Option’s Delta 📈

The thing that gives options traders the most excitement is when the price of the underlying asset changes suddenly, making their contracts worthless. But if traders only wanted excitement, all hedge funds would have trampolines in their offices (which they don’t—we know this for a fact). Actually, every trader’s priority is their bottom line, and that is why delta is so important.

Delta measures how much an options contract’s price will be changed by a $1 movement in the underlying stock. This means that knowing our option’s delta gives us the ability to predict how much money we will win or lose if scenarios A, B, or C play out—and with markets becoming riskier and riskier as time goes on, risk management is more important than ever.. 

Moreover, delta is used for hedging—once a trader knows how much they might lose if their trade goes south, they know how much to invest in a hedge to offset that risk. Here is how delta is calculated and what it means.

Calculating the Delta 🧮

Options sellers use delta to figure out how to price their options and to do so, they need to measure how sensitive an option is to changes in the underlying’s price. This is done by using the following formula:

Formula used to calculate option’s delta
Delta is a ratio that compares the change in an underlying asset’s price with the price change of a derivative or option.

Simply, by using this formula we can just see how much the underlying’s price changed and how much the options price has changed since the option was first sold. Then, it is easy to divide the two to get the ratio at which changes in the underlying affect the option’s value.

Here is an example—let’s say we buy a call option for Apple stock. At that moment in time, AAPL costs $300 and the option’s strike price is $310—the options contract itself cost us $40. 

A bit later, the stock goes to $320, and our option is suddenly profitable. If the option rises in value and goes to $42, that means its delta, according to the formula, is: 

= ($42 – $40) \ ($320 – $300) 

= $2 \ $20 

= 0.1. 

This means that every time the underlying’s price changes by $1, the option’s price changes by $0.1.

Determining Profitability 💵

Now that we’ve calculated delta, we know how much changes in the underlying’s value impact our option’s price—and that way, we know how much we can sell our option for. If optimistic news about a new Apple product comes out and the stock becomes worth $20, that means that the option itself will be worth $2 more.

Directional Risk ♻

If the Apple stock from our example rises by $1 the option will be worth $0.1 more—but that also works in reverse. Delta also tells us how much we stand to lose if the underlying drops by a certain amount.

If AAPL is very volatile and can move $100 up or down, this means that an option with a high delta for this stock carries a lot of risk but also a lot of potential. To offset that risk, we can buy a hedge for our call position—and its value will be based on the option’s delta. 

In other words, if the delta of a call option is really high and the underlying seems like it will go down in the future, we can hedge that position by buying a put option. This way, no matter the direction in which the underlying moves, we will make some money and that will offset any losses. This is a common way of eliminating directional risk.

Option’s Gamma 📏

If you think that delta is complicated, you’ll love gamma. Namely, gamma is the rate at which an option’s delta changes when the underlying asset moves by one point (when it comes to stocks, one “point” means one dollar). So, gamma can tell us how much delta will change if the underlying’s price moves by X dollars.

We’ll show you how it works.

Calculating the Gamma 📝

The formula for gamma follows the same logic as delta’s formula. Here it is:

Formula to calculate an option’s gamma
Gamma is used to determine how sensitive an option is to price changes and it is one of the metrics used in determining an option’s value.

Let’s look at an example to understand this. Let’s say again that Apple is trading at $320 and we have a call option with a delta of 0.3. A bit later, the stock jumps to $330 and our option’s delta is now 0.5. Here is how this can help us find the gamma:

Γ = (Δ1 – Δ2) \ (P1 – P2)

Γ = (0.3 – 0.5) \ ($320 – $330)

Γ = (-0.2) \ (-$10)

Γ = 0.02

Option’s Vega 📉

Vega is a very special Greek because it is not actually a letter in the Greek alphabet—finance people just made the term up because they wanted something that starts with ‘V’ to represent volatility (and maybe they were Street Fighter fans). Namely, vega is the measure of how sensitive an option’s price is to implied volatility.

Vega tells us how much a 1-point change in volatility will change the option’s price. If an option has a high vega, that means that its value will change significantly if its implied volatility changes.

Calculating the Vega ✏

Remember how we said that vega isn’t a letter in the Greek alphabet? Well, its symbol is the Greek letter N (nu), but its lower-case version looks like a V, so all that kind of makes sense. Here is the vega formula:

Formula used to calculate vega
Vega measures an option’s sensitivity to implied volatility.

We will stick to our AAPL example. Let’s say that the price of our option was $45 when we bought it and is now $50. Let’s also say that the implied volatility of the option was 15% beforehand, and is now 20%. Here is how we can calculate vega using this info:

v = (P1 – P2) \ (σ1 – σ2)

v = ($45 – $50) \ (15% – 20%)

v = (-$5) \ (-5%)

v = 1

Therefore, every time implied volatility changes by %1, our option’s value changes by 1%. A high vega is neither good nor bad, it just tells us how sensitive the option is. 

Option’s Theta 📅

The final piece of the equation is time decay, a.k.a. an option’s theta. Options lose value as they draw closer to their expiry date and that has to be taken into account when planning options trades.

Theta is the ratio of time decay—it tells us how much value our option will lose with each day that goes by. For example, if the option is worth $10 and its theta is 0.05, tomorrow, that option will be worth $9.95. Note that theta is generally expressed as a negative value for long positions and positive for short positions.

Calculating the Theta 🖊

The formula for calculating theta (Θ) is as follows:

Formula used to calculate an option’s theta
Theta refers to an option’s rate of decline in value as time goes by.

So if our Apple option was worth $45 when we bought it—at this time, it had 30 days left until expiry. Now, 10 days later, it is worth $40 and has 20 days left to expiry. That means we can calculate the rate of time decay as follows:

Θ = (O1 – O2) \ (τ1 – τ2)

Θ = – (($45 – $40) \ ( 30 days – 20 days))

Θ = – ($5 \ 10 days)

Θ = -$0.5/day

It seems like our option loses half a dollar for each day that goes by, as theta indicates. Unlike other Greeks that are neither good nor bad, a high theta is generally a negative factor—if an option loses value rapidly due to time decay, it will be in lower demand than a more durable options contract.

🤓 Keep in mind: All of the premier stock trading apps provide Greeks on all listed options contracts, so there is no need to calculate these figures manually.

An Explanation of Minor Greeks 👨‍🏫

None of the Greeks used in options trading get as much love as the four that we’ve just discussed but there are more of them. The chief among them and the most commonly used is rho (ρ).

Rho is used to measure how the price of an option is impacted by a 1% change in interest rates. As interest rates don’t change that often, rho is a fairly niche Greek—but when interest rates are all over the place as they have been after the COVID crash, rho suddenly becomes very important.

If you are a gamer, this will look like a list of runes from the Diablo series—here are some of the more commonly seen second-order Greeks as well as their functions:

  • Lambda (λ) – Measures how much leverage an option provides as its price changes
  • Epsilon (ε) – Measures how sensitive the option is to changes in the underlying’s dividend yield
  • Vomma (vomma) – Measures how sensitive an option’s vega is to changes in implied volatility
  • Vera (vera) – Measures the changes in an option’s price, rho, and vega due to changes in volatility and interest rates
  • Color (color) – Measures the rate at which gamma will change over time
  • Ultima (ultima) – Measures how sensitive an option’s vomma is to changes in volatility

Final Word: The Importance of Understanding Greeks 🏁

The first thing to know about Greeks is that you don’t need to calculate them—they are automatically provided on every modern brokerage platform, so the trader only needs to understand them. However, understanding them is crucial because Greeks tell us if an options contract is fairly valued by its seller and we can avoid bad deals.

Moreover, knowing whether to sell an options contract before its expiry and when to sell it is a lot easier when we have Greeks to tell us how to value the contract. All in all, understanding Greeks might be a bit of a headache in the beginning, but this knowledge can separate a novice from a serious options trader.

Options Greeks: FAQs

  • What Are the Greeks in Options Used For?

    Greeks are used to measure the sensitivity of an option’s price to changes in market volatility, underlying asset’s price, and time to expiry. All these metrics impact the prices of options contracts.

  • What Are the Best Greeks for Options?

    The most commonly used Greeks in options trading are delta, gamma, and theta. In combination, these 3 metrics can tell the trader how sensitive their options contract’s value is to price changes in the underlying stock, and how the contract is impacted by its time to expiry.

  • How Many Greeks Are There in Options?

    Only 4 Greeks are used specifically for options trading: gamma, delta, theta, and vega. Greeks other than these four are used for analyzing the underlying asset’s price, but not the price of the options contract itself.

  • What is a Good Implied Volatility?

    The usual implied volatility of an S&P index fund is around 30%. This is the market average that most traders aim for, but the ideal measure of implied volatility will depend on the trader’s strategy and risk tolerance.

  • Is High IV Good for Options?

    High implied volatility makes the options contract more sensitive to the price changes in the underlying stock. In other words, an option with a high IV will gain or lose more value with each price swing in the underlying asset—this makes an option riskier and more potentially profitable. 

  • Why is Vega Highest at the Money?

    Vega is the highest when the strike price and the underlying price are near each other. Moreover, vega gradually declines as the option nears expiration, and is the highest when there is a lot of time left until expiry.

  • Is Negative Theta Good?

    Whether a negative theta is good or not depends on the trader’s intentions and strategy. A negative theta, as opposed to a positive theta, simply means that an option’s value will decrease relatively quickly as it approaches its expiry date.

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