Option value calculator (Black-Scholes)
Enter the underlying price, strike, expiration, volatility, rate and an optional dividend yield to get the Black-Scholes model value and the full set of Greeks, computed in your browser. The risk-free rate prefills from the US Treasury yield curve at the tenor nearest your expiration — always editable. Arriving from an option-chain row also prefills that contract’s implied volatility and shows Cboe’s own delayed theoretical value alongside ours for comparison.
Inputs, and what the model does with them
- S / K / T: underlying price, strike, and time to expiration in years (calendar days ÷ 365).
- σ (volatility): the annualized volatility assumption — the input the model is most sensitive to; chain links prefill the contract’s implied volatility.
- r (risk-free rate): prefilled from the daily US Treasury par yield curve at the tenor nearest T; q is a continuous dividend yield and may be left blank.
- Delta/gamma describe price sensitivity, theta is the per-day time decay, and vega/rho are sensitivities to a 1% change in volatility/rates — all per share.
- The model assumes European exercise and constant volatility; listed US equity options are mostly American-style with discrete dividends, so traded prices can deviate — Cboe’s own delayed theoretical value renders alongside for comparison.