Option Greeks Made Easy: Delta, Gamma, Vega, Theta, Rho

Option Greeks Made Easy: Delta, Gamma, Vega, Theta, Rho


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What Are Options Greeks

Option greeks

Option contracts have fast-paced price action, and to a beginner, their movements won’t always make sense. If you’ve ever questioned why, “The stock went up, but my bullish option position went down!” Then it’s time you got familiar with the option greeks.

There are five different greeks — delta, gamma, vega, theta, and rho — and they all hold important clues about the option contracts that they represent. Understanding these five option metrics will help you to determine how your option will react to changes in volatility, time, and the stock price — which in turn will help you to better plan your trades.

Delta – It’s All About the Dollar Move

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First, here’s the technical definition of delta: The amount an option price is expected to move based on a $1 change in the underlying stock.

How Options Delta Works: Option’s Price VS Underlying Stock Price

You buy a call option for $1.50 with a delta of 0.50. The share price of the underlying stock immediately shoots higher by $2.00. You can expect your option to gain roughly $1.00 in value — making it $2.50.

The caveat to the above example: Delta isn’t the only greek that goes into pricing an option. As you’ll discover throughout this article, option greeks like gamma, vega, theta, and rho will also have something to say about the effects of these price movements. But still, measuring dollars-to-deltas is a good way to get a rough estimate of your option’s potential price movement.

If that all went over your head — that’s okay. Let’s explain it in a couple of other ways:

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Options Delta Explained: Delta is Like a Car

If your option was a car, delta would be the speed at which your car was driving. If you have a low delta, your car is driving slowly. For instance, an option with a delta of 0.01 is going to increase in value at a much slower rate than an option with a delta of 0.75. For each dollar that the stock moves higher, the 0.75 delta option is racing higher 75 cents — at the same time, the option with the delta of 0.01 is only gaining 0.01 cents.

One more interesting way to think of delta is as a measure of probability.

An Option’s Delta As a Measure of Probability

Many view delta as a measure of an option contract’s likelihood of expiring in-the-money. If a stock’s price is $100, and the strike price of a call option is $10 — the option’s delta is probably going to be pretty close to 1.00. That’s because it’s pretty likely that the stock is going to expire above $10.

That’s why at-the-money option contracts are typically at or near the 0.50 delta — there’s about a 50/50 chance that the contract expires in-the-money. Keep in mind, the option’s delta is not representative of an option’s probably of profit — an option can expire in the money and still not be “profitable”. Delta is only a proxy measurement of an option’s likelihood of expiring in the money, rather than out of the money.

Gamma — How Fast the Delta Moves

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Gamma and delta are closely related. It’s gamma’s job to determine the rate at which delta moves higher or lower according to dollar moves in the underlying stock.

How Options Gamma Works: Option’s Price Example

You buy a call option for $1.50 with a delta of 0.50 and a gamma of 0.05. The share price of the stock rises by $1.00. Now you have an option with a delta of 0.55. To get that calculation, we multiplied the gamma (0.05) by the dollar move (1.00), and then added it to the old delta value (0.50), giving us our new delta of 0.55. By now, we should know what that means — if the delta is 0.55, it means the option premium will increase by $0.55 for each $1.00 move in the underlying stock.

If all the equations have you feeling like you’re in a high school math class — don’t worry. Here’s an easier way to think about gamma:

Options Gamma Explained: Gamma is Like the Acceleration of the Car

If your option was a car, and delta was the speed at which you were driving, gamma would be the acceleration. Your speed was just $0.10 for every dollar move in the underlying stock, but as the stock keeps rising, gamma is pressing down on the gas, raising the speed of your option’s price movement. When the stock starts to run, gamma pumps your delta up, allowing the option price to change faster. 

One more note about gamma is that it becomes more volatile as an option contract nears expiration. As time ticks by, the probability of OTM options expiring in-the-money starts to deplete faster and faster. But a speedy swing in share price could quickly turn a losing short-term option around — and that’s thanks to gamma.

Speaking of time’s effect on option prices…

Unusual Options Activity

Theta — Hostile to Option Holders, Friendly to Option Sellers

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If you’re only familiar with one of the greeks, it’s probably theta. Theta is synonymous with time, and if you didn’t know already: if you’re long options, time is not your friend. For long options theta is represented as a negative value, representing the amount of premium that will drain from an option each day.

However, unlike delta and gamma, getting out the calculator and running the numbers on a specific theta value isn’t really feasible — theta values rely on an assumption that the implied volatility and price movement of a will remain constant. Spoiler alert: they won’t.

Rather than taking theta literally, it’s better to think about the theta curve.

When Does Theta Decay Kick In

option greeks

Basically, as time goes on, theta speeds up, little by little. More than 60 days out from expiration? It’s not very fast. But once an option passes 60 days, the curve begins to steepen, further steepening at 30 days, and reaching “max velocity” at 14 days.

For premium collectors (people who sell options), that 14-day zone is the sweet spot. For long option holders, that 14-day zone is just the opposite — a high-risk area. As we said above, short-term options can provide big moves in price in either direction, which is why some traders love them. But if you’re not experienced, this high-risk zone can lead to rapid declines in the price of your option.

Want another way to think about theta? Let’s go back to our car example.

Options Theta Explained: Theta is Like the Gas in the Car

Recall that if an option was a car, delta would be the speed at which the car was moving. Gamma would be the acceleration of the car’s speed. Theta is like the amount of gas in your tank. You want to keep an eye on how much time you have left on the road before you need to refuel. (Roll your option to a further expiration, anyone?)

Of course, this isn’t a perfect example — gas doesn’t start rapidly depleting the lower your fuel gauge goes. But think about that sense of panic when you’re driving with a tank that’s almost empty, and you can’t find a gas station. That’s how it feels to watch theta creep up on your option.

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Theta isn’t kind to long options, but here’s a greek that is:

Vega — V is for Volatility

You know the drill. Technical definition first: Vega measures the change in option premium based on 1% changes in implied volatility.

Implied volatility (or IV) isn’t an option greek, but it is another important factor that goes into determining how much an option costs. Implied volatility is basically the market’s best guess at the likely movement of a security.

When the market starts to price in bigger price swings in a stock, the implied volatility will rise accordingly — which will in turn increase the vega. If you’re long options, that’s a good thing. If you’re a premium collector, you want vega to get down and stay down.

So for example, an option contract has a vega of 0.10, and an implied volatility of 100%. Suddenly, the IV drops to 90%. The IV decreased by -10 percentage points — multiply that by the vega (0.10), and we get a dollar value of -$1.00. Your option premium decreased by a dollar just because of a decrease in volatility!

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What is Implied Volatility Crush (IV Crush)

Think that’s bad? Try holding an option through an earnings event. Just before earnings, implied volatility is high — the market is pricing in a high probability of a big move in the underlying stock. After the earnings report is released, IV rapidly depletes, a phenomenon known as IV crush. This causes vega values to decrease in unison, which work against the price of an option.

It’s important to note that vega has a much greater pull on out-of-the-money options since OTM options are all extrinsic value.


Do you know the difference between extrinsic and intrinsic value? You can think of intrinsic value as “what the option would be worth if it expired immediately,” and extrinsic value as “what could happen between now and expiration.”

Example: Imagine you have a $100 stock and a $99 strike call option. The $99 strike call option is priced at $3.00. That means you have $1.00 of intrinsic value (the value of the option if it expired right now), and $2.00 of extrinsic value (the value assigned to the option based on what the market predicts could happen — in this case, the market is pricing in the probability that the stock moves to $102 by expiration.) An OTM option has 0 intrinsic value.

We could say Vega is the “potential for bumps in the road” or something, but let’s be honest, the car analogy has run out of gas. You’re a pro now, and you don’t need a fancy comparison to understand this one. Vega is just the likelihood of volatility. Before earnings, or when the VIX is elevated, vega is often higher. After earnings, or when the VIX is suppressed, vega is often lower.

So now you understand delta, gamma, theta, and vega. These are the four greeks that everyone cares about. But there’s one more that people don’t often think of…

Rho — The One Everyone Forgets About (The R is for Rate)

There’s a reason most traders don’t pay attention to this greek: it has the smallest pull on your option’s value compared to the other four — especially if you’re trading options on a medium or short-term time horizon. But it’s still important to paint the full picture of option greeks, and if you’re buying into long-duration assets like LEAPS, rho is something you’ll want to be aware of.

Rho measures the rate that an option changes in value relative to 1% changes in interest rates. Long calls are positive rho, long puts are negative rho. So if your rho is 4.00, and interest rates rise by 0.25%, you can expect your option to increase in value by $1.00 — thanks rho!

Rho has a greater impact on long-term options than short-term options, and on in-the-money options more than out-of-the-money options. While rho can make a difference in the price of your option, it isn’t really that important to keep an eye on. Interest rates don’t move at the same rate as, for instance, IV does.

The Bottom Line: Delta, Gamma, Theta, Vega, Rho

Understanding these five greeks goes a long way in being able to understand your overall portfolio positioning — especially if you’re deploying multiple separate option strategies.

For instance, you might have some long calls (which are positive delta, gamma, vega, rho, and negative theta) in the same portfolio as a short iron condor (which is neutral delta, gamma, and rho, negative vega, and positive theta).

Being able to accurately gauge your portfolio’s total delta or total vega can go a long way when you’re planning your next move — and allow you as a trader more potential areas to gain an edge.

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