The Greeks: Quick Reference

The four option Greeks at a glance, each with what it measures and what it means for a premium seller. Jump to the one you need. For the concepts behind these terms, see Options Terminology.

A Greek measures how an option’s price responds to a change in one input, holding the others fixed. The signs below are for the short position the income seller holds: one call sold against shares (a covered call) or one put sold against set-aside cash (a cash-secured put).

The four Greeks

Greek	Measures (per unit change)	Sign for a short option	What it means for the income seller
Delta	Option price, per $1 move in the underlying	Negative (short call); positive (short put)	How fast the position moves against you as the stock approaches your strike; also a rough proxy for assignment odds (see below).
Theta	Option price, per day of time passing	Positive	Time decay is the seller’s income mechanic: the extrinsic value you sold erodes in your favor each day, all else equal.
Gamma	Delta, per $1 move in the underlying	Negative	How sharply your delta swings near the strike; highest at the money close to expiration, which is why a small late move can flip the outcome.
Vega	Option price, per 1-point move in implied volatility	Negative	After you sell, a rise in implied volatility marks your short option up against you; a fall marks it down in your favor.

Delta

First-order Greek. The change in an option’s price for a $1 change in the underlying. A call delta runs 0 to 1; a put delta runs -1 to 0.

For the seller: delta is sometimes read as a rough proxy for the odds the option finishes in the money, and therefore for the odds of assignment, but it is an approximation, not a direct probability or a measurement. A short call with a 0.30 delta sits roughly 30% as a rough proxy, not a 30% measured chance of being called away.

Theta

First-order Greek. The premium an option loses per day from time decay, all else equal. Negative for a long option, which makes it positive for the seller who is short it.

For the seller: theta is the mechanic behind selling premium. The extrinsic (time) value in the premium you collected erodes toward zero by expiration, and that erosion accrues to you. See Time Decay.

Gamma

Second-order Greek. The change in delta for a $1 change in the underlying, so it measures how fast delta itself moves. Largest for at-the-money options near expiration.

For the seller: high gamma near expiration means your delta, and so your assignment exposure, can swing on a small stock move. It is the reason a position that looked safe a week out can become live in the last days.

Vega

First-order Greek. The change in an option’s price for a one-point change in implied volatility. Negative for the seller, who is short the option.

For the seller: you collect more premium when implied volatility is high, because a wider expected range makes the option more valuable. After you have sold, a further rise in implied volatility raises the option’s price against your short position; a fall lowers it in your favor.

The context the Greeks live in

The Greeks describe how a premium moves; these three terms describe what the premium is and what drives it. Each links to its full treatment.

Intrinsic vs. extrinsic value

A premium splits into two parts. Intrinsic value is the amount the option is in the money (for a call, stock price minus strike; for a put, strike minus stock price), never below zero. Extrinsic value, also called time value, is the rest: the part that reflects time remaining and volatility. Theta erodes the extrinsic part; an out-of-the-money option is entirely extrinsic. See Options Terminology.

Implied volatility

The market’s expectation of how much the underlying will move over the option’s life, backed out from the option’s current price and expressed as an annualized percentage. Higher implied volatility means a higher premium. It is the input vega measures sensitivity to, and it is forward-looking, distinct from realized (historical) volatility. See Options Terminology.

Moneyness

Where the strike sits relative to the current stock price: in the money (has intrinsic value), at the money (strike near the stock price), or out of the money (no intrinsic value yet). Moneyness sets how much of a premium is intrinsic versus extrinsic, and it tracks roughly with delta. See Options Terminology.