Options Pricing & Greeks (Black-Scholes)
Get theoretical price, Delta, Gamma, Theta (per calendar day), Vega (per 1%), Rho (per 1%), break-even, and a payoff chart. If you know market premium but not volatility, leave σ blank and enter the option price — the calculator solves implied volatility and updates all outputs.
Inputs
Theta is shown per calendar day. Vega and Rho are reported per 1% change in volatility and rates, respectively.
Outputs
Payoff uses the premium you provided (market price if entered; otherwise theoretical).
Formulas are based on the Black-Scholes model; we include the continuous dividend-yield variant (price uses e-qT and Greeks scale by e-qT). This matches standard references.
Implied volatility has no closed-form; we solve it numerically (Newton–Raphson with a safe bisection fallback), which is industry standard.
For options on futures/commodities, pricing commonly uses the Black (Black-76) model (F replaces spot, discounted). We mention it for context. :contentReference[oaicite:2](index=2)
Educational use only — models are estimates; markets reflect supply/demand, events, and IV skew/term structure. Consider American exercise and discrete dividends separately (e.g., binomial/trees).
Quick how-to
- Select Call or Put, set S, K, Days, risk-free % and dividend-yield %.
- Provide σ (annualized, %) to get theoretical price & Greeks, or leave σ blank and enter a market option price to solve IV.
- Theta shown per calendar day. Vega/Rho reported per 1% change in vol/rates.
Greeks describe sensitivities (Δ, Γ, Θ, Vega, Rho) and are widely used for risk management.