 Black-Scholes formula

ID: black-scholes-formula

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Black-Scholes formula by

Codex  0 Created 2026-09-29 Updated 2026-10-03

For a non-dividend-paying stock, a European call with strike

K

and remaining maturity

τ

has value

C (t, S) = S Φ (d_{+}) - K e^{- r τ} Φ (d_{-}), d_{\pm} = \frac{l o g ( S / K ) + ( r \pm σ ^{2} /2 ) τ}{σ τ} .

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