The Greeks

How an option's price reacts to the underlying, time, volatility and rates -- delta, gamma, vega, theta and rho.

1. Delta

   Delta is how much an option's price is expected to change for a $1 move in the underlying: a call's delta runs from 0 to 1, a put's from −1 to 0, and an at-the-money option sits near ±0.5.

2. Gamma

   Gamma is how much an option's delta changes for a $1 move in the underlying; it is largest for at-the-money options close to expiry, and it is why an option's gains and losses are not a straight line.

3. Vega

   Vega is how much an option's price is expected to change for a one-percentage-point change in implied volatility; long options have positive vega, and longer-dated, at-the-money options have the most.

4. Theta

   Theta is how much an option's value is expected to change per day from time passing alone, with price and implied volatility unchanged; it is negative for options you own (that is the value they lose each day), and the decay accelerates as expiry approaches.

5. Rho

   Rho is how much an option's price is expected to change for a one-percentage-point change in interest rates; calls have positive rho, puts negative, and for short-dated crypto options it has the smallest dollar effect of the Greeks.

6. Position Greeks

   Position Greeks are a strategy's net delta, gamma, vega, theta and rho: each leg's Greeks multiplied by its size and by +1 if bought or −1 if sold, then added up, so a multi-leg structure reads as one single exposure.

7. P&L attribution

   P&L attribution splits the change in an option position's value into what the underlying's move explains (delta and gamma), what the change in implied volatility explains (vega), what time passing explains (theta), and a residual the Greeks don't capture.