What each one measures
| Greek | Answers | Unit here |
|---|---|---|
| Delta | how much the option moves per $1 of the underlying | per share |
| Gamma | how much delta itself moves per $1 | per share |
| Theta | what a day of waiting costs | per day |
| Vega | what one point of IV is worth | per 1% of IV |
| Rho | sensitivity to interest rates | per 1% of rates |
All are per share. Multiply by the contract multiplier — usually 100 — for one contract.
Units are where these go wrong
The model produces theta annualised and vega per 1.00 of volatility. Both are useless in that form, and both are quoted differently by different platforms, which is how a position gets sized against a number that is out by two orders of magnitude.
- Theta per year divided by 365 is theta per day. The raw figure is 365× larger.
- Vega per 1.00 of vol divided by 100 is vega per 1%. The raw figure is 100× larger.
This calculator does both conversions and says so in the row labels. If a number here disagrees with your platform by roughly 100 or 365, the units are the reason, not the model.
How they behave, which is the useful part
Delta runs from 0 to 1 for calls, 0 to −1 for puts, and sits near 0.5 at the money. It is often read as a rough probability of finishing in the money — close enough for intuition, not identical to it.
Gamma peaks at the money and rises sharply as expiry approaches. This is why a short-dated at-the-money position feels unstable: delta changes so fast that a hedge set at the open is wrong by lunchtime.
Theta is largest at the money and accelerates in the final weeks. It is not linear — the last month decays far faster than the month before it, which is the whole basis of selling short-dated premium.
Vega is largest for long-dated options and falls towards expiry. A weekly option barely notices a volatility change; a six-month option is dominated by it. This is why a long call can be right about direction and still lose after an earnings release, as IV collapses.
Gamma and theta are the same trade
Read together, these two describe every option position honestly.
Long options are long gamma, short theta: you gain from movement and pay for time. Short options are short gamma, long theta: you collect time and pay for movement.
There is no position that is long both, and every strategy that appears to be one is short gamma somewhere with the risk pushed further out. Knowing which side you are on tells you what kind of market ends you — and it is a more useful thing to know than any individual number in the table.