Black-Scholes call option price

Gives the theoretical price of a European call option on a non-dividend-paying stock under the Black-Scholes model. It is used to value European options and to compute implied volatility.

C = S_{0} N (d_{1}) - K e^{- r T} N (d_{2})

C = S_0 N(d_1) - K e^{-rT} N(d_2)

What the symbols mean

$C$	price of the call option
$S_{0}$	current price of the underlying asset
$K$	strike price of the option
$r$	continuously compounded risk-free interest rate
$T$	time to expiration in years
$N (\cdot)$	cumulative distribution function of the standard normal distribution
$d_{1}$	\frac{\ln(S_0/K)+(r+\sigma^2/2)T}{\sigma\sqrt{T}}
$d_{2}$	d_1 - \sigma\sqrt{T}
$σ$	volatility of the underlying asset's returns

About this formula

FieldEconomics and finance
TopicOption pricing
LevelUniversity
Also calledBlack-Scholes formula, Black-Scholes call price, European call option price, Black-Scholes option pricing model, BSM call formula, option pricing formula

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