BLKSHCLPRC Function

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

Category: Financial
Returned data type: DOUBLE
Syntax
Arguments
Details
Comparisons
Example
See Also

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
S
is a nonmissing, positive value that specifies the share price.
N
specifies the cumulative normal density function.
E
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:
t
specifies the time to expiration, in years.
r
specifies the risk-free interest rate, which is an annual rate that is expressed in terms of continuous compounding.
sigma
specifies the volatility (the square root of the variance).
sigma squared
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

See Also

Functions:
BLKSHPTPRC Function
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