Options Pricing & Greeks (Black–Scholes)
Get theoretical price, Δ, Γ, Θ (per calendar day), Vega (per 1%), Rho (per 1%), break-even and a payoff chart. If you know the market premium but not σ, leave it blank and provide the option price—the calculator solves implied volatility and updates all outputs.
Inputs
Θ is per calendar day. Vega/Rho are per 1% change. Current moneyness: ATM.
We use the dividend-yield variant (terms scale with e−qT) and show Θ per calendar day. Greeks and prices follow closed-form Black–Scholes.
Educational use only — models are estimates; markets include skew/smile and American exercise/discrete dividends not captured by B-S.
Quick how-to
- Choose Call or Put; set S, K, days, r% and q%.
- Enter σ% for theoretical results, or leave σ blank and enter a market premium to solve IV.
- Use payoff shading, P(ITM), and the what-if slider to explore scenarios.
Outputs
Payoff uses the premium you provided (market price if entered; otherwise theoretical).
How to use the Black-Scholes calculator
Estimate option fair value and sensitivity to key variables. Before calculating, enter accurate inputs: Enter spot price, strike, time, volatility, rates, and option type.
After you get the output, interpret it like this: Use price and Greeks to understand directional and time risk. Practical tip: Model output is sensitive to volatility assumptions.This calculator is for planning and scenario analysis, so use it with your broader risk management, position sizing, and market context before taking a real trade or investment decision.
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