Black-Scholes Call Price Calculator
Price a European call option with the Black–Scholes formula — enter spot, strike, volatility, rate and time to see the fair premium, d1, d2 and delta.
How it works
C = S·N(d1) − K·e^(−rT)·N(d2) · d1 = [ln(S/K) + (r + σ²/2)T] ÷ (σ√T) · d2 = d1 − σ√T
The Black–Scholes formula prices a European call as the expected payoff at expiry, discounted to today. N(d1) and N(d2) are risk-neutral probabilities from the standard normal distribution — N(d1) is also the call’s delta, the amount the premium moves per $1 move in the underlying. Higher volatility or more time both lift the price, because they widen the range of favourable outcomes without adding downside beyond the premium paid.
Worked example
At spot $100, strike $100, 20% volatility, a 0% rate and one year to expiry: d1 = (ln 1 + 0.02)/0.20 = 0.10 and d2 = −0.10, so N(d1) = 0.5398 and N(d2) = 0.4602. C = 100 × 0.5398 − 100 × 0.4602 = $7.97 per share.
Sources: Black–Scholes model (Wikipedia)
Frequently asked questions
Why is an at-the-money call worth so much with zero intrinsic value?
When spot equals strike the intrinsic value is zero, so the entire premium is time value — the chance the stock finishes above the strike before expiry. With 20% volatility and a year to run, that optionality is worth roughly $8 per share.
Does this include dividends?
No. This is the classic Black–Scholes model for a non-dividend-paying stock. A dividend yield would lower the call price; you would replace S with S·e^(−qT) in the formula.
Is this for American or European options?
European — exercisable only at expiry. For non-dividend-paying stocks an American call is never worth exercising early, so the two prices match. American puts can differ.
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Educational estimate using a simplified Black–Scholes / options model — no dividends, no early-exercise, no fees or slippage. Options are high-risk. Not investment advice.