# BLKSHPTPRC Function

Calculates put prices for European options on stocks, based on the Black-Scholes model.

 Category: Financial

## Syntax

BLKSHPTPRC(E, t, S, r, sigma)

### Required Arguments

#### E

is a nonmissing, positive value that specifies the exercise price.

 Requirement Specify E and S in the same units.

#### t

is a nonmissing value that specifies the time to maturity.

#### S

is a nonmissing, positive value that specifies the share price.

 Requirement Specify S and E in the same units.

#### r

is a nonmissing, positive fraction that specifies the risk-free interest rate for period t.

 Requirement Specify a value for r for the same time period as the unit of t.

#### sigma

is a nonmissing, positive fraction that specifies the volatility of the underlying asset.

 Requirement Specify a value for sigma for the same time period as the unit of t.

## Details

The BLKSHPTPRC function calculates the put prices for European options on stocks, based on the Black-Scholes model. The function is based on the following relationship:
$equation$
Arguments
S
is a nonmissing, positive value that specifies the share price.
E
is a nonmissing, positive value that specifies the exercise price of the option.
$equation$
The following arguments apply to the preceding equation:
t
specifies the time to expiration.
r
specifies the risk-free interest rate for period t.
$equation$
specifies the volatility (the square root of the variance).
$equation$
specifies the variance of the rate of return.
For the special case of t=0, the following equation is true:
$equation$
For information about the basics of pricing, see Using Pricing Functions.

## Comparisons

The BLKSHPTPRC function calculates the put prices for European options on stocks, based on the Black-Scholes model. The BLKSHCLPRC function calculates the call prices for European options on stocks, based on the Black-Scholes model. These functions return a scalar value.

## Example

The following SAS statements produce these results.
SAS Statement
Result
`----+----1----+-—-2--`
```a=blkshptprc(1000, .5, 950, 4, 2);
put a;```
`16.385367922`
```b=blkshptprc(850, 1.2, 125, 3, 1);
put b;```
` 1.426971358`
```c=blkshptprc(7500, .9, 950, 3, 2);
put c;```
`273.45025684`
```d=blkshptprc(5000, -.5, 237, 3, 2);
put d;```
`           0`