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Black-Scholes (Call Option)

Prices a European call option, where d₁ and d₂ depend on the stock price, strike, volatility, rate and time. N(·) is the standard normal CDF.

Formula

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

CCall price

S₀Current stock price

KStrike price

rRisk-free rate

TTime to expiry

NNormal CDF

Higher volatility or more time to expiry both raise the option’s value

The Black-Scholes model earned Scholes and Merton the 1997 Nobel Prize in Economics (Black had died in 1995).