Options Greeks: delta, gamma, theta, vega and rho

Written by the Tactfolio research teamPublished Data as of 7 min read

The options Greeks are five numbers that show how an option’s price should change when one thing changes and everything else stays the same. Delta covers the stock price, gamma covers how fast delta moves, theta covers time, vega covers expected swings, and rho covers interest rates. They are estimates from pricing models, not promises.

Key points#

  • Each Greek answers one “what if” question about an option’s price.
  • Many traders look at delta first. It shows how much the option moves when the stock moves $1.
  • Option buyers lose a little to theta every day. Sellers collect it.
  • The Greeks change all the time as the stock, the clock and the market’s mood change.
  • One standard US stock option covers 100 shares, so multiply each Greek by 100 for one contract.

Risk note. Options can expire worthless. Selling options can lose far more than the premium you collect.

What are the Greeks in options?#

The Greeks are sensitivity numbers. Each one estimates how much an option’s price, called its premium, would change if one input moved a set amount. They get their names from Greek letters, except vega, which is not a real Greek letter.

GreekWhat it measuresRound-number example (per share)
DeltaChange in option price for a $1 move in the stockDelta 0.50: stock up $1, call up about $0.50
GammaChange in delta for a $1 move in the stockGamma 0.05: stock up $1, delta goes from 0.50 to 0.55
ThetaChange in option price for one day passingTheta −0.05: one day later, option down about $0.05
VegaChange in option price for a 1 point move in implied volatilityVega 0.15: volatility up 1 point, option up about $0.15
RhoChange in option price for a 1 point move in interest ratesRho 0.10: rates up 1 point, call up about $0.10

These numbers come from option pricing models. Your broker’s option chain usually shows them next to each strike. The Options Industry Council explains each one in more depth.

If calls and puts are new to you, start with put vs call. It covers strike prices, premiums and expiration with simple examples.

Delta: how much the option moves with the stock#

Delta tells you how many cents the option should move for each $1 move in the stock. Call deltas run from 0 to 1. Put deltas run from 0 to −1, because puts gain when the stock falls.

Example. Say you own a call with a delta of 0.50. The stock rises $1. The call should rise about $0.50 per share, or $50 for one contract. If the stock falls $1, the call should drop about $50.

An option with a strike near the stock price usually has a delta near 0.50 (or −0.50 for a put). Deep in-the-money options move closer to 1, almost like the stock. Far out-of-the-money options sit closer to 0.

Gamma: how fast delta changes#

Gamma tells you how much delta itself will change when the stock moves $1. It is the speed of delta.

Example. Your call has a delta of 0.50 and a gamma of 0.05. The stock rises $1. Delta climbs to about 0.55. Now the next $1 rise adds about $0.55, not $0.50.

The Options Industry Council notes that gamma is highest for options with a strike near the stock price, especially close to expiration. That is when an option’s value can swing the most in a single day.

Theta: what time costs#

Theta is how much value an option loses each day as its end date gets closer. It is shown as a negative number for someone who owns the option.

Example. A put costs $2.00 per share and has a theta of −0.05. If nothing else changes, it is worth about $1.95 tomorrow. That is $5 a day for one contract.

Time decay speeds up as expiration nears. Our guide to theta shows how it works and why sellers like it.

Vega: what expected swings are worth#

Vega shows how much an option’s price changes when implied volatility moves 1 percentage point. Implied volatility is how much the market expects the stock to swing, worked out from option prices.

Example. The Options Industry Council uses an option worth $4 with a vega of 0.15. If implied volatility rises 2 points, the option should gain about $0.30, to about $4.30. If it falls 5 points, the option should lose about $0.75.

Both calls and puts gain when implied volatility rises. Our guide to implied volatility explains why options get cheaper right after earnings news.

Rho: what interest rates do#

Rho shows how much an option’s price changes when interest rates move 1 percentage point. It is positive for calls and negative for puts.

Example. A call has a rho of 0.10. Rates rise from 4% to 5%. The call should gain about $0.10 per share, or $10 a contract. A put with a rho of −0.10 would lose about the same.

For short-dated options, rho is usually the smallest Greek. The Options Industry Council notes it matters more for longer-dated options.

Putting the Greeks together: one example#

Real prices move with all the Greeks at once. Here is one day for a single call.

Say a stock trades at $50. You own one call with a $50 strike. It costs $2.00 per share. Its delta is 0.50, gamma 0.05, theta −0.04 and vega 0.10.

The next day, the stock rises $1 and implied volatility does not change.

  • Delta adds about $0.50. Gamma adds a little more, about $0.03, because delta grew during the move.
  • Theta takes away about $0.04.
  • Vega adds nothing, because volatility did not change.

The new price is about $2.49 per share, or $249 for the contract. That is an estimate. The real price can differ.

Common mistakes#

  • Reading delta as a sure thing. Delta is a model estimate. Real prices also depend on supply and demand.
  • Forgetting that Greeks change. A delta of 0.50 today can be 0.80 next week.
  • Ignoring theta on short-dated options. A cheap option with a week left can lose value fast even if the stock does not move.
  • Buying right before big news. Implied volatility often drops after earnings, and vega works against the buyer.
  • Selling options without a plan for the worst case. A covered call limits that risk with shares you own. A call sold without shares has no loss limit.

Try it on Tactfolio#

Tactfolio does not trade or backtest options, so you cannot test the Greeks here. Some people use options to limit losses in a falling market. One idea without options is a trend rule. The 200-day moving average strategy holds the S&P 500 above its 200-day average and Treasury bills below it. As of September 25, 2026, its hypothetical backtest from mid-2007 had a worst fall of about 22%, against 55% for the S&P 500. It also returned less, about 8% a year against 11%. You can read every rule and build your own version in the strategy builder.

Common questions#

Which option Greek is most important?#

No single Greek matters most for everyone. Many traders start with delta, because it shows how the option reacts to the stock. Theta matters a lot for short-dated options. Vega matters around big news, such as earnings.

What is a good delta for options?#

There is no good or bad delta. A delta near 0.50 means the strike is close to the stock price. A higher delta acts more like the stock. A lower delta costs less but is less likely to finish in the money.

Do options Greeks work the same for calls and puts?#

Mostly, but the signs differ. Calls have positive delta and puts have negative delta. Both lose to theta when you own them and gain when implied volatility rises.

Where do I find the Greeks for an option?#

Most brokers show them in the option chain, next to each strike price. They come from a pricing model, so different brokers may show slightly different numbers.

Why is vega not a Greek letter?#

Vega is not in the Greek alphabet. Traders use the name anyway, because it fits with the other Greeks and starts with a V, like volatility.

The details#

  • Most brokers compute the Greeks with a model in the Black and Scholes family, using the stock price, strike, time left, interest rate and implied volatility.
  • Delta and gamma are first and second rates of change with respect to the stock price. Theta, vega and rho are rates of change with respect to time, volatility and the interest rate.
  • Quoted values are per share and per unit: one dollar, one day, one percentage point. Multiply by 100 for a standard contract.
  • Before trading options, US brokers must give you the Options Clearing Corporation’s booklet, Characteristics and Risks of Standardized Options.

Sources

Put it into practice