An option is not the stock. Its price can change because the stock moved, because time passed, because fear was repriced, or because rates moved. Greeks are nicknames for those five. They are estimates, not promises. Teaching numbers only — not live quotes. Not financial advice. This site never places orders, and it will omit a Greek rather than invent one.
One teaching call: XYZ $100, $100 strike, $3.00, 30 days. Delta 0.50, gamma 0.08, theta −0.05, vega 0.12, rho about 0.01. Chain quotes are per share. Multiply by 100 for dollars per contract. A 0.40 delta is about $40 if the stock moves $1. Same idea for the others. The lab below uses the same teaching Black–Scholes as What if — move the stock and the curves update.
Chain quotes often list delta as 0.40 meaning $40 per $1 stock move per contract (×100). Same idea for the others: multiply the per-share Greek by 100 to get dollars per contract.
Delta
Calls: 0 to 1 · Puts: 0 to −1
How much the option moves when the stock moves
Delta is the first-speed number. If the stock goes up $1, a call with delta 0.40 tends to gain about $0.40 per share ($40 per contract). A put with delta −0.40 tends to lose about $0.40 if the stock rises $1, and gain if the stock falls. Picture it as a share-equivalent: 0.50 delta is like being long 50 shares — until gamma moves that number.
Example: XYZ is $100. You buy a $100 call for $3.00 with delta 0.50. XYZ jumps to $102. The call might be worth about $4.00 (up $1, which is 0.50 × $2). You did not get the full $2 the stock moved — options usually move a fraction of the stock.
Deep in-the-money calls have delta near 1 (they act like stock). Far out-of-the-money calls have delta near 0 (they barely budge).
Gamma
Always a positive number for long options
How fast delta itself changes
Gamma is acceleration. After the stock moves, delta is not the same number it was a minute ago. High gamma means delta can swing quickly — common near the strike and near expiration. That is why a 2-day ATM option feels jumpy and a 90-day far-OTM option barely notices the same tick.
Example: That same $100 call had delta 0.50 and gamma 0.08. XYZ rises $1. Delta may become about 0.58 (0.50 + 0.08). The next $1 up in XYZ helps the call more than the last $1 did. If XYZ falls $1, delta may drop to about 0.42, so the next drop hurts less than a full 0.50 would suggest.
Short options have negative gamma: the move that just happened tends to make the next move worse for you. That is why short premium near expiration can feel jumpy.
Theta
Usually negative if you bought the option
What you pay (or collect) for one day of waiting
Options expire. Theta is the slow leak (or drip of income) from time passing, if nothing else changes. Buyers usually pay theta. Sellers usually collect it — and take delta, gamma, and vega in return. The clock is not linear: the last two weeks often cost more per day than the first month.
Example: Your $3.00 call has theta −0.05. If XYZ sits still overnight, the call might be worth about $2.95 tomorrow ($5 less per contract). Over 10 quiet days that can be $50 gone, even with no news. A short put with theta +0.05 is the other side of that clock.
Theta speeds up in the last couple of weeks. A 60-day option decays slowly; a 5-day option can melt in a hurry if it is not in the money.
Vega
Long options have positive vega
How much the option cares about implied volatility
Vega is not the stock going up or down. It is how scared (or calm) the market is priced to be. Implied volatility up → option prices usually up. Implied volatility down → option prices usually down, even if the stock did not move. Longer-dated options have more vega. That is why a vol crush after a print can erase a correct directional bet.
Example: Your call has vega 0.12. Implied volatility rises 5 points (for example 20% to 25%). The call might gain about $0.60 per share ($60 per contract) from vega alone. If IV (implied volatility) crashes 5 points after earnings, that same $60 can vanish even if XYZ is unchanged.
This is why the site may stand aside into earnings: you can be right on direction and still lose if IV (implied volatility) collapses. We never invent a vega if the delayed chain does not show one.
Rho
Usually the smallest Greek for short-dated stock options
How much interest rates matter
Rho is the interest-rate Greek. Higher rates tend to help calls a little and hurt puts a little, because carrying stock with cash has a cost. For 30-day single-stock options, rho is often tiny compared with delta, theta, and vega.
Example: A one-year $100 call might have rho 0.20. If rates rise 1 percentage point, that call might gain about $0.20 per share. A 30-day call on XYZ might show rho near 0.01 — a $1 rate move is about a dollar per contract. Useful to know; rarely the main story on this desk.
Ignore rho until you are trading long-dated options or the Fed is moving in big steps. Still learn the name so a chain quote does not look like a mystery.