Black-Scholes Calculator
European OptionsReal-time theoretical call & put pricing, exact Greeks, intrinsic breakdown, and payoff graphs.
Quick Presets:
⚙️ Parameter Inputs
$
$
days
%
%
%
💡 How Black-Scholes Calculations Are Done
Prices and Greeks are calculated in real-time using the closed-form Black-Scholes-Merton model with continuous dividend yields ($q$):
Call: S · e⁻𝑞ᵀ · N(d₁) - K · e⁻ʳᵀ · N(d₂)Evaluates upside stock participation vs strike.
Put: K · e⁻ʳᵀ · N(-d₂) - S · e⁻𝑞ᵀ · N(-d₁)Evaluates downside protection value vs strike.
The cumulative normal distribution $N(x)$ is solved using the Abramowitz & Stegun approximation ($|error| < 7.5 \times 10^-8$), ensuring microsecond quantitative accuracy.
Call OptionEuropean
$0.000
Theoretical Value
Intrinsic$0.00
Time Value$0.00
Put OptionEuropean
$0.000
Theoretical Value
Intrinsic$0.00
Time Value$0.00
📊 Option Greeks & Sensitivity
Continuous Model| Greek | Sensitivity | Call Exposure | Put Exposure |
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