Beyond the option’s price itself, the Greeks measure exactly how that price reacts to a change in each individual input.
How it works
Using the same d1/d2 terms this site’s Black-Scholes price calculator computes, standard partial-derivative formulas give delta (sensitivity to the stock price), gamma (how delta itself changes), vega (sensitivity to volatility), and theta (value lost per day).
What this does not include
This does not include put option Greeks (delta, in particular, differs by exactly 1 for a put versus a call at the same strike and expiry) or rho, the sensitivity to interest rate changes, which this calculator omits as typically the least-watched Greek in practice.
How to use this calculator
- Enter spot price, strike price, risk-free rate, volatility, and time to expiry.
A worked example
A call option with spot price $100, strike $100, 5% risk-free rate, 20% volatility, 1 year to expiry: delta = 0.6368, gamma = 0.0188, vega = 0.3752, theta = −0.0176.
What the variables mean
| Variable | Meaning |
|---|---|
| Delta | How much the option price changes per $1 move in the underlying |
| Gamma | How much delta itself changes per $1 move in the underlying |
| Vega | Sensitivity to a 1% change in volatility |
| Theta | Time decay — value lost per day as expiration approaches |
Edge cases worth knowing
Theta is negative for a long option position — options lose value as time passes, all else equal, which is exactly why theta is shown as a negative number here rather than positive.
Zero volatility makes the Greeks undefined — an option on a completely riskless underlying has no meaningful sensitivity to price or volatility changes, so the calculator declines to show a result.
Frequently asked questions
Why do traders care about gamma specifically?
Gamma shows how fast delta itself will change as the stock moves — a high-gamma position needs to be re-hedged more frequently to stay delta-neutral.
Is theta always negative for a long option position?
For a long (bought) option, yes — time decay works against the option holder every day, all else equal, which is what theta measures.
How is vega different from the other Greeks?
Vega measures sensitivity to a change in the market’s volatility expectation itself, not to the underlying’s actual price movement — a genuinely different risk dimension from delta or gamma.
