The Black$-$Scholes option pricing model is C$=$SN$($d$\_\{1\})-$Xe$^\{-$rt$\}$N$($d$\_\{2\}).$ This formula follows the basic theorem of finance where the value of the call is equal to the present discounted value of expected future cash flows. In the Black$-$Scholes formula N$($d$1)$ and N$($d$2)$ represent:

probabilities used in calculating the expected value.

factors related to continuous time.

expected cash flows.

discount factors.