The option Greeks
An option's price depends on the stock, the time left, and implied volatility, and all three change every minute. The Greeks are the sensitivities: each says how much the price moves when one of them moves and the rest stand still. Together they describe what a position is really a bet on.
Delta: the stock
Delta is how much the option's price moves for a $1 move in the stock: from 0 to 1 for calls, from −1 to 0 for puts. An at-the-money option has a delta near ±0.50; a deep in-the-money one near ±1, moving almost like the stock; a far out-of-the-money one near 0.
- Share equivalent. One contract covers 100 shares, so delta × 100 is how many shares it acts like for a small move: a 0.30-delta call behaves like 30 shares.
- A rough probability. Delta is close to the market's odds of the option finishing in the money: a 0.25-delta call about one in four. This is why strikes are named by delta, as in the 25-delta put of the skew.
Gamma: how fast delta changes
Gamma is how much delta changes for a $1 move in the stock, the curvature of the position. Bought options have positive gamma: delta grows as the stock moves your way and shrinks as it moves against you, so moves help. Sold options have negative gamma: every move pushes delta the wrong way, so calm helps. Gamma is largest at the money and close to expiry, which is why a short at-the-money option on its last day can swing from worthless to deep in the money in minutes. Summed over a whole market's open interest, gamma becomes dealer gamma exposure.
Theta: the clock
Theta is how much the option loses in a day as time passes, everything else unchanged. Bought options have negative theta, sold options positive. Decay is not even: time value shrinks roughly with the square root of the time left, so it speeds up toward expiry, most sharply for at-the-money options in the last few weeks.
time value ∝ √(time left) → half of a 60-day option's time value is gone with ~15 days left
Vega: implied volatility
Vega is how much the price changes for a one-point move in implied volatility. Bought options are long vega and gain when IV rises; sold options are short vega. Vega is largest at the money and grows with time to expiry, so long-dated options ride on IV most. A vega of 0.12 and an IV up 3 points add about $0.36 a share, $36 a contract. It is vega that makes an option bought before earnings lose money in the IV crush.
Rho and dividends
Rho is the change for a one-point move in interest rates: higher rates raise calls and lower puts. It is small for short-dated options and matters for LEAPS a year or more out. Dividends work the other way: an expected dividend lowers calls and raises puts, since the stock drops by it on the ex-date and option holders do not receive it.
Reading a position's Greeks together
The Greeks of a position are the sums of its legs', and they trade off. Positive gamma is paid for with negative theta: you pay every day for the chance that a move helps. Negative gamma is paid with positive theta: you are paid every day to carry the risk of a move. A short strangle, for one, is short gamma, short vega, and long theta, a bet that the stock sits still and IV falls. Across many positions, add them up: a book of short puts in different names is one large long-delta, short-gamma bet in a sell-off.
In Options Meerkat
The Black-Scholes calculator (%) opens on the contract under the cursor and gives its price, delta, gamma, theta, vega, and implied volatility from inputs you can change. A strategy's P/L page (p on a symbol's detail page) shows its net Greeks, and its date line and IV scaling (v, V) show theta and vega at work on the curve. The portfolio page (P) sums the Greeks of your open trades per symbol, delta in shares and dollars and theta in dollars a day, and the IV surface (V, then $) can show every contract's Greeks at once.