Option Greeks measure an option's sensitivity to changes in the underlying price, time, volatility, and interest rates. Public calculates Greeks and implied volatility in real time, in-house — they are not sourced from a third party. Market data used as input comes from our market data provider.
Greeks are computed with the Black–Scholes model. Implied volatility is solved by inverting the Bjerksund–Stensland (2002) approximation, which accounts for dividends and early exercise.
| Greeks | Black–Scholes (European exercise) |
| Implied volatility | Bjerksund–Stensland 2002 inversion (American exercise; accounts for dividends and early exercise) |
| Dividends | Continuous dividend yield |
| Option price used | Midpoint, (bid + ask) / 2, with fallback to last trade when a two-sided quote isn’t available |
| Solver | Hybrid Newton–Raphson / Brent root-find — Newton–Raphson for fast convergence, falling back to bracketing + Brent for robustness |
The bracketing + Brent fallback also handles edge cases such as near-zero volatility and numerical instability.
| Convention | Calendar days between now and expiration, divided by 365.25 |
| 0DTE floor | Floored at 0.000002 years (≈63 seconds) so Greeks remain finite as the contract approaches expiration |
Note this is a calendar-time clock, not a trading-time (252-day / market-hours) clock.
Measures: Sensitivity to a $1 change in the underlying price.
The theoretical estimate of how much an option's value may change given a $1 move up or down in the underlying security. Values range from -1 to +1, with 0 representing an option whose premium barely moves relative to price changes in the underlying.
Measures: Rate of change of delta per $1 move in the underlying.
Represents the rate of change between an option's delta and the underlying asset's price. Higher gamma values indicate that delta could change dramatically with even small price changes in the underlying.
Measures: Sensitivity to the passage of time (time decay).
Indicates the amount an option's price would decrease as the time to expiration decreases, all else equal. Time is measured using the calendar-time convention described above.
Measures: Sensitivity to a 1% change in implied volatility.
Measures the amount of increase or decrease in an option premium based on a 1% (one volatility point) change in implied volatility.
Measures: Sensitivity to a 1% change in interest rates.
Represents the rate of change between an option's value and a 1% change in the interest rate.
Greeks are returned as part of the greeks object — containing delta, gamma, theta, vega, rho, and impliedVolatility — in two places:
optionDetails.greeks.📝 Notes