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Black-Scholes Option Pricing Calculator

Price a European call or put option using the Black-Scholes-Merton formula, from the spot price, strike, risk-free rate, volatility, and time to expiration.

Call option price
$10.45
Put option price
$5.57
d1
0.35
d2
0.15

How it works

The Black-Scholes-Merton model prices a European option (one that can only be exercised at expiration) from five inputs: the spot price S, strike K, risk-free rate r, volatility σ, and time to expiration T. It computes d1 = (ln(S/K) + (r + σ²/2)T) / (σ√T) and d2 = d1 − σ√T, then Call = S·N(d1) − K·e^(−rT)·N(d2) and Put = K·e^(−rT)·N(−d2) − S·N(−d1), where N is the standard normal cumulative distribution function.

This assumes the underlying pays no dividends, volatility and the risk-free rate stay constant through expiration, and the option can't be exercised early — the standard simplifying assumptions behind the original model. It prices what an option is theoretically worth today, which is a different question from this site's options payoff calculator, which shows profit/loss at expiration for an option you've already bought at a known premium.

FAQ

Why do I need to supply volatility — isn't that something the calculator should know?

Volatility is the one input the market doesn't observe directly; it's an estimate of how much the underlying price is expected to swing before expiration, often derived from historical price data or from the market price of similar options (implied volatility). This calculator takes it as a given input rather than guessing at a current market value, consistent with this site's rule against inventing real-world data.

Does this account for dividends or early exercise?

No — this is the original Black-Scholes model for a European option on a non-dividend-paying asset. American options (exercisable anytime) and dividend-paying underlyings need extensions to this model that aren't included here.

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