BLKSHCLPRC Function

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

Category:	Financial
Returned data type:	DOUBLE

Syntax

Syntax

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

Arguments

E

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

Requirement	Specify E and S in the same units.
Data type	DOUBLE

t

is a nonmissing value that specifies the time to maturity, in years.

Data type

INTEGER

S

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

Requirement	Specify S and E in the same units.
Data type	DOUBLE

r

is a nonmissing, positive value that specifies the annualized risk-free interest rate, continuously compounded.

Data type

DOUBLE

sigma

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

Data type

DOUBLE

Details

The BLKSHCLPRC function calculates the call prices for European options on stocks, based on the Black-Scholes model. The function is based on the following relationship:

table with 1 row and 1 column , row1 column 1 , c eh l l , equals s n . open , d sub 1 , close . minus e n . open , d sub 2 , close . epsilon super negative r t end super , end table

Arguments

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

specifies the cumulative normal density function.

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

$table with 2 rows and 2 columns , row1 column 1 , d sub 1 , equals , column 2 fraction open natural log of . open , s over e , close . plus . open r plus , fraction sigma squared , over 2 end fraction , close . t close , over sigma square root of t end fraction , row2 column 1 , d sub 2 , equals , column 2 d sub 1 , minus sigma square root of t , end table$

The following arguments apply to the preceding equation:

specifies the time to expiration, in years.

specifies the risk-free interest rate, which is an annual rate that is expressed in terms of continuous compounding.

specifies the volatility (the square root of the variance).

specifies the variance of the rate of return.

For the special case of t=0, the following equation is true:

table with 1 row and 2 columns , row1 column 1 , , column 2 c eh l l , equals mehx of . open . open s minus e close . comma 0 close , end table

For information about the basics of pricing, see Using Pricing Functions in SAS Functions and CALL Routines: Reference.

Comparisons

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

Example

The following statements illustrate the BLKSHCLPRC function:

Statements	Results
	----+----1----+-—-2--
select blkshclprc(50,.25,48,.05,.25);	1.79894201954463
select blkshclprc(9,1/12,10,.05,.2);	1

BLKSHCLPRC Function

Syntax

Arguments

E

t

S

r

sigma

Details

Comparisons

Example

See Also