What are the options Greeks?

An option price comes from a handful of inputs: the stock price, the strike, the time left, implied volatility, interest rates and dividends. The Greeks take those inputs one at a time and ask a simple question: if only this one changes, how much does the premium change? That makes them a risk dashboard, not a forecast.

Three things to keep in mind. They are quoted per share, so multiply by 100 for one standard contract. They are model estimates that hold everything else still, while in a real market several inputs move at once. And they change constantly: the delta you read at the open is not the delta you hold at noon. If calls and puts are still new to you, start with options trading for beginners and call vs put.

Turn your phone sideways to read the drawing. Tap to close.

A hand-drawn dashboard of four cards for the guide’s hypothetical $100 call (stock at $100, 30 days, IV 30%, worth about $3.59): delta 0.53, a $1 rise adds about $0.53; gamma 0.05, a $1 rise lifts delta from 0.53 to about 0.58; theta −0.06, one day passing takes about $0.06; vega 0.11, one point more IV adds about $0.11. A footnote adds rho 0.04, and that values are per share, × 100 for one contract.

What is delta in options?

Delta estimates how much the option moves for a $1 move in the underlying stock or ETF. Call deltas run from 0 to 1 and put deltas from 0 to −1, because puts gain when the stock falls. An at-the-money option sits near 0.50 (or −0.50 for a put), a deep in-the-money option moves toward 1.00 and a far out-of-the-money option toward 0.

In our example the $100 call has a delta of 0.53. If the stock rises from $100 to $101, the call should gain about $0.53, from $3.59 to roughly $4.12. The model actually says $4.15, because gamma adds a little as delta grows. If the stock falls $1, the call loses about $0.50. The matching $100 put has a delta of about −0.47: it gains roughly $0.47 when the stock drops $1 and loses about as much when the stock rises $1.

Delta also works as a share equivalent. For small moves, one call with a 0.53 delta behaves like about 53 shares (0.53 × 100), and three contracts like about 160 shares. That is the quickest way to compare an options position with the stock trade you would otherwise take. For a buyer, delta answers one question: how much of the stock move do I capture? A higher delta captures more of each dollar but costs more premium. A lower delta is cheaper but needs a bigger move to pay off.

Is delta the probability of expiring in the money?

Many traders read delta as a rough probability that the option finishes in the money at expiration: a 0.30-delta call as roughly a 30% chance, a 0.50-delta call as roughly a coin flip. It is a handy shortcut, and only a shortcut. Four caveats:

  • It comes from a model that assumes implied volatility is right and that returns follow a bell curve. Real stocks gap, trend and react to news in ways the model does not capture.
  • It is not even the model's own probability. In our example the 0.53-delta call has a model probability of finishing in the money of about 50%, and a $110 call with a 0.15 delta about 13%.
  • In the money is not the same as profitable. A call buyer who holds to expiration needs the stock above the strike plus the premium paid, which is less likely than just finishing above the strike.
  • It moves with every tick and every day, so a 0.30 delta today says little about next week.

What is gamma, and why does it explode near expiration?

Gamma is the rate of change of delta: how much delta moves for a $1 move in the stock. Our 30-day $100 call has a gamma of about 0.05, so a $1 rise lifts its delta from 0.53 to roughly 0.58. Gamma is highest for at-the-money options and grows as expiration gets close.

Near expiration it gets extreme. The same $100 call with one day left is worth about $0.63, with a delta of 0.51 and a gamma of about 0.25, more than five times the 30-day figure. A $1 rise takes its delta to about 0.74 and its price to about $1.26, roughly double. A $1 drop takes its delta to about 0.27 and its price to about $0.25, a loss of about 60%. Within hours, the option is deciding between being worth something and being worth nothing.

For a buyer, gamma works both ways. When the stock moves your way, rising delta makes each extra dollar count for more. When it moves against you, falling delta shrinks what is left. That two-sided speed is what makes 0DTE options so fast, and why position size matters even more with them than with longer-dated contracts.

What is theta decay? Why time decay speeds up into expiration

Theta estimates how much an option loses per day from the passage of time, with the stock price and implied volatility unchanged. Our 30-day call has a theta of about −0.06, roughly $6 per contract per day. For a buyer, theta is the rent you pay for holding the position.

Over a one-hour scalp, that rent barely registers. Over a two-week swing in a short-dated contract, it can eat most of the premium even if the stock eventually goes your way. A time stop, closing the trade if the move has not come by a set time, is how buyers cap the rent.

Theta decay is not linear. It speeds up as expiration approaches, most of all for at-the-money options. Hold the stock at $100 and the call loses about $1.58 between day 60 and day 30, then its whole remaining $3.59 in the last 30 days. The same hypothetical $100 call, stock unchanged, IV at 30%:

  • 60 days left: about $5.17, losing about $0.05 a day.
  • 30 days left: about $3.59, losing about $0.06 a day.
  • 14 days left: about $2.42, losing about $0.09 a day.
  • 7 days left: about $1.70, losing about $0.12 a day.
  • 1 day left: about $0.63, losing about $0.32 a day.

What is vega? How implied volatility moves the price

Vega estimates how much the option's price changes for a one-percentage-point change in implied volatility (IV), the market's priced expectation of how much the stock will move. Our call has a vega of about 0.11. If IV rises from 30% to 35% with the stock unchanged, the call gains roughly 5 × $0.11, about $0.57 per share or $57 a contract. If IV drops from 30% to 25%, it loses about the same, even though the stock did not move.

Longer-dated options carry more vega than short-dated ones: in our model a 90-day at-the-money call has a vega of about 0.20, a 7-day call about 0.06. Buyers of calls and buyers of puts both have positive vega, so both are hurt when IV falls.

The classic trap is earnings. IV tends to build before the report and drop sharply after it, so a buyer can be right on direction and still lose. The full story, with a worked example and how to compare IV with its own history, is in our implied volatility guide.

What is rho?

Rho estimates the change in the option price for a one-percentage-point change in interest rates. It is positive for calls and negative for puts: higher rates tend to lift call premiums and lower put premiums. Our 30-day call has a rho of about 0.04, so a full one-point move in rates would change its price by about four cents.

Rates rarely move a full point during the life of a short-dated option, so most day traders and swing traders can set rho aside. It matters more for options with many months or years left, where the effect builds with time.

Options Greeks cheat sheet

The short version for anyone buying calls or puts. All values are per share; multiply by 100 for one contract.

  • Long call: positive delta, positive gamma, negative theta, positive vega.
  • Long put: negative delta, positive gamma, negative theta, positive vega.
  • At the money: the most gamma, theta and vega in dollar terms.
  • Close to expiration: gamma and theta speed up, vega shrinks.
  • Far from expiration: more vega, slower theta, gamma is calmer.
Delta
Delta is the estimated change in an option's price for a $1 move in the underlying. Calls range from 0 to 1, puts from 0 to −1, and at-the-money options sit near 0.50 either way. Multiplied by 100, it is the option's rough share equivalent.
Gamma
Gamma is the estimated change in delta for a $1 move in the underlying. It is highest for at-the-money options close to expiration, which is why short-dated options can swing so fast.
Theta
Theta is the estimated change in an option's price for one day passing, with nothing else changing. For a buyer it is negative, and the decay speeds up as expiration approaches.
Vega
Vega is the estimated change in an option's price for a one-point change in implied volatility. Option buyers lose from a drop in implied volatility, as often happens after earnings.
Rho
Rho is the estimated change in an option's price for a one-point change in interest rates. It is positive for calls, negative for puts and matters mostly for long-dated options.

How do the Greeks change for ITM, ATM and OTM options?

Moneyness reshapes the whole profile. In-the-money (ITM) options behave most like the stock: high delta and little time value, so theta and vega are small next to the premium. At-the-money (ATM) options carry the most gamma, theta and vega in dollars. Out-of-the-money (OTM) options are cheap, have a low delta and lose the largest share of their value to time each day. Our guide on how to choose a strike price builds on this.

As expiration nears, ITM deltas drift toward 1.00, ATM deltas stay near 0.50 and OTM deltas fall toward 0. A rise in implied volatility pulls deltas the other way, toward 0.50. Here is the same $100 stock, 30 days out, IV 30%, across three call strikes (hypothetical model values):

  • $90 call (in the money): about $10.70, delta 0.90, theta −0.03 a day, about 0.3% of its price.
  • $100 call (at the money): about $3.59, delta 0.53, theta −0.06 a day, about 1.7% of its price.
  • $110 call (out of the money): about $0.66, delta 0.15, theta −0.035 a day, about 5% of its price.
  • Reading across: the cheap $110 call loses the fewest dollars per day but the largest share of its price, and at expiration it needs the stock above $110.66 just to break even.

Turn your phone sideways to read the drawing. Tap to close.

Three hand-drawn delta dials from 0 to 1 for calls on a $100 stock with 30 days left and IV at 30%: the $90 call (in the money) at delta 0.90, about $10.70, theta −0.03; the $100 call (at the money) at 0.53, about $3.59, theta −0.06; the $110 call (out of the money) at 0.15, about $0.66, theta −0.035. Red bars show the daily decay as a share of the price: about 0.3%, 1.7% and 5%.

How to use delta to choose contracts for scalps and swings

Start from the chart, not the options chain. A trade plan on the underlying gives you an entry, a stop and a target in stock prices. Delta converts those distances into option dollars, and theta tells you what waiting costs. Our options scalping strategy and swing trading options guides build on this frame.

Scalp, hypothetical: the stock is at $100, with a target at $102 and a stop at $99, held minutes to an hour. With 30 days left, decay over an hour is tiny, so delta and gamma do the work. The $100 call (delta 0.53) would gain about $1.16 at the target and lose about $0.51 at the stop. The $110 call (delta 0.15) would gain about $0.36 and lose about $0.14: smaller dollars, and on a $0.66 option a few cents of bid-ask spread is a large share of the trade. The $95 call (delta 0.75) captures the most of each dollar, about $1.57 up and $0.74 down, for a higher premium.

Swing, hypothetical: same stock, target $106 and stop $97, expected to take about five days. Five days later, a 45-day $95 call bought at about $7.39 (delta 0.72) would be worth about $12.04 at the target, $5.12 at the stop and $7.15 if the stock were still at $100. A 7-day $100 call bought at about $1.70 would be worth about $6.02 at the target, but about $0.09 at the stop and $0.90 if the stock went nowhere: time alone would cost it almost half. More time costs more premium up front and buys slower decay; that trade-off is yours to weigh.

The chart step is where UpTickFlow fits, and only that step. It runs on the chart of the underlying and draws an entry, a stop and a target before the trade; it does not read options data, choose strikes or expirations, or place orders. You still pick the contract, size it and exit the option when the underlying reaches the stop or the target. The Greeks are how you check whether that contract fits the plan. Any option you buy can lose its whole premium, so size every position so that a total loss is a cost you planned for. To see a contract's outcome at expiration, try the options profit calculator.