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Valuation of a European call option (Black & Scholes model) formula

Description of the Valuation of a European call option (Black & Scholes model) formula

Formula for the evaluation of a European call option on an underlying which does not pay dividends before the expiry of the option, using the Black & Scholes model

Formula

\[ c(s,t) = SN(d1) - Ke^{-rt}N(d2) \] \[ {\small where: d1 = \frac{ln \left( \frac{S}{K} \right ) + \left(r+\frac{\sigma^{2}}{2}\right)t}{\sigma\sqrt{t}} ;} \] \[ {\small d2 = d1 - \sigma \sqrt{t} } \ \]

Symbols

\(K\ \)       
Option strike price
\(N\ \)       
Standard normal cumulative distribution function
\(r\ \)       
\(σ\ \)       
\(S\ \)       
Price of the underlying
\(t\ \)       
Time to option's expiry