Black function is useful to compute prices given by Black-Scholes model.
This function is available in R-code (here). See also its upper level page (here).
Definition 1 A black function
is given by
where
is a normal random variable for some
and
is either
or
.
R-code is written according to the following fact:
Proposition 2 Let
be c.d.f. of standard normal distribution. Then,
where