The options Greeks measure how an option's price responds to the forces that move it: Delta to the stock price, Gamma to changes in Delta, Theta to the passage of time and Vega to implied volatility. For a stock trader, they translate an option position into familiar terms: share equivalents, daily cost and exposure to volatility.
How it works
Delta: the share equivalent
Delta is the approximate change in an option's price for a $1 move in the stock. Calls range from 0 to 1 and puts from 0 to −1; an at-the-money option sits near ±0.50. Because a standard US contract covers 100 shares, a delta of 0.50 behaves like 50 shares. Delta is also often used as a rough proxy for the chance that the option expires in the money; it is only an approximation.
Gamma: how fast Delta changes
Gamma is the change in Delta for a $1 move in the stock. It is highest for at-the-money options close to expiry. Buying options gives you positive gamma, so favorable moves add exposure; selling options gives you negative gamma, so adverse moves add exposure. Summed across the market, dealer gamma underlies gamma exposure.
Theta: the cost of time
Theta is the change in an option's value from one day passing, with everything else unchanged. It is negative for option buyers and positive for sellers, and for at-the-money options it accelerates in the final weeks before expiry.
Vega: exposure to volatility
Vega is the change in an option's price for a one-point change in implied volatility. Longer-dated options have more vega. A position can be right on direction and still lose money if implied volatility falls, as it often does after earnings (see IV crush).
A fifth Greek, Rho, measures sensitivity to interest rates and matters mainly for long-dated options.
| Greek | What it measures | Long call | Long put | Short call or put |
|---|---|---|---|---|
| Delta | Price change per $1 stock move | Positive | Negative | Opposite of the long |
| Gamma | Delta change per $1 stock move | Positive | Positive | Negative |
| Theta | Price change per day | Usually negative | Usually negative | Usually positive |
| Vega | Price change per 1-point rise in IV | Positive | Positive | Negative |
How to read it
- Size with Delta. Converting a position to share equivalents makes it comparable with a stock position of the same risk.
- Respect Gamma near expiry. Short options close to expiry and near the money can swing from small to large exposure within one session.
- Weigh Theta against the move you need. A long option pays Theta every day, so the stock must move enough, soon enough, to cover it; the expected move shows how much movement is already priced in.
- Check Vega before events. Options bought before earnings carry high implied volatility that usually falls once the news is out.
Worked example (illustrative numbers)
A stock trades at $100. A 30-day at-the-money $100 call with implied volatility of 30% is worth about $3.43 under the Black–Scholes model (interest rates and dividends ignored). Its Greeks:
| Greek | Per share | Per contract (100 shares) | Meaning |
|---|---|---|---|
| Delta | 0.52 | 52 share equivalents | A $1 rise adds about $52 |
| Gamma | 0.046 | 4.6 shares per $1 | After a $1 rise, Delta is about 0.56 |
| Theta | −$0.057 a day | −$5.70 a day | Value lost if nothing moves for a day |
| Vega | $0.11 per IV point | $11.40 per IV point | IV from 30% to 35% adds about $57 |
If the stock rises to $101, the call is worth about $3.97: a gain of $0.54 a share, slightly more than Delta alone suggests, because Gamma raises Delta along the way. If implied volatility instead drops 10 points after an event, the call loses roughly $1.14 a share, or $114 a contract, even with the stock unchanged.
Limitations and common mistakes
- Greeks are local. They describe small changes from today's inputs; for large moves, the actual change differs.
- They interact. Delta changes with price, time and volatility, so yesterday's Greeks can be stale.
- They are model outputs. Different models, volatility inputs and dividend assumptions give somewhat different values, and US equity options can be exercised early.
- Delta is not a probability. It is a reasonable rough guide to the chance of expiring in the money, not an exact figure.
- Quotes matter. Greeks computed from wide or delayed bid/ask quotes inherit their errors.
In Clear Tape
In the strategy builder on the Options page, Pro members see Greeks for the whole position, one lot, in plain words: Delta as a share equivalent, Gamma as the change in Delta per $1, Theta as the dollar amount earned or lost per day if nothing moves, and Vega per one-point change in implied volatility. The legs table shows each leg's Delta, a Delta control moves the strikes to those nearest a chosen Delta, and the chance of touching a short strike is shown with the rule of thumb of about twice its Delta. Greeks use the Black–Scholes model and are estimates from delayed quotes; members see each session's closing data once the next session has opened. See pricing.
For educational purposes only. Not investment advice.