There are a number of assumptions underlying the formula:
Based on these assumptions, it is possible to derive their
C = P × N(d1)-EX×e-rt×N(d2),
where
C = the value of the call option
N(d) = the cumulative normal probability density function
EX = the exercise price of the option
σ2 = the variance per period of continuously compounded rate of return on stock
t = the time to the maturity date
r = the continuously compounded risk-free rate of interest
P = the price of the stock now