Black-Scholes Options Pricing
Calculate call and put option prices and all five Greeks (delta, gamma, theta, vega, rho) using the Black-Scholes model. Enter spot price, strike, volatility, rate, and expiry.
Call price
$8.01
Put price
$6.03
Δ call
0.5799
Δ put
-0.4201
Γ
0.02211
Vega (per 1%)
0.2764
Θ call (per day)
-0.0244
Θ put (per day)
-0.0137
ρ call (per 1%)
0.2499
ρ put (per 1%)
-0.2402
How to use the black-scholes options pricing
Enter the underlying price (S), strike (K), time to expiry in years (T), risk-free rate, volatility, and dividend yield. Call and put prices appear with all five Greeks for each.
Formula & explanation
Black-Scholes-Merton (with dividends): C = Se^(-qT) N(d1) − Ke^(-rT) N(d2). Vega is per 1% vol change; Theta is per day; Rho is per 1% rate change.
Examples
S = K = 100, T = 0.5 yr, r = 4%, σ = 25%: call ≈ 7.97, put ≈ 5.99 (no dividends).
Frequently asked questions
- Why use this vs. real market prices?
- For pricing illiquid options, computing fair value, and estimating sensitivity (Greeks). Real markets price implied vol; our σ is your assumption.
- American options?
- Black-Scholes assumes European exercise. American options on non-dividend stocks are equivalent for calls; for puts and dividend-paying stocks, use a binomial tree.
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