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

* *

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