Black-Scholes Option Pricing Calculator
Price European call and put options with the Black-Scholes formula. Enter spot price, strike, time to maturity, rate, and volatility to instantly get d1, d2, and the theoretical values.
Input
$
$
yr
%
%
Result
Call price
$8.92
Put price
$6.94
d₁
0.2000
d₂
0.0000
N(d₁) (call delta)
0.5793
N(d₂) (exercise probability)
0.5000
Call price
$8.92
Put price
$6.94
How it works
- The Black-Scholes model computes the theoretical call and put prices of non-dividend-paying European options (exercisable only at maturity).
- Call price C = S0·N(d1) − K·e^(−rT)·N(d2), and put price P = K·e^(−rT)·N(−d2) − S0·N(−d1), where N() is the cumulative distribution function of the standard normal distribution.
- d1 = (ln(S0/K) + (r + σ²/2)T) / (σ√T) and d2 = d1 − σ√T, where S0 = spot price, K = strike price, T = time to maturity (years), r = risk-free rate, and σ = volatility.
- Enter the rate and volatility as annualized percentages (%); they are converted to decimals internally. Enter the time to maturity in years (e.g., 6 months = 0.5).
- The standard normal CDF is computed with an error-function approximation, so a very small numerical error may occur. Dividends, transaction costs, and early exercise of American options are not considered.
- Note: This tool provides theoretical values for educational and reference use only. Actual market prices may diverge from the model's assumptions. Make investment decisions at your own risk.
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Black-Scholes Option Pricing Calculator