BLACKCLPRC Function

Calculates call prices for European options on futures, based on the Black model.

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

Syntax

BLACKCLPRC(E, t, F, r, sigma)

Arguments

E

is a nonmissing, positive value that specifies exercise price.

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

t

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

Data type DOUBLE

F

is a nonmissing, positive value that specifies future price.

Requirement Specify F 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 (the square root of the variance of r).

Data type DOUBLE

Details

The BLACKCLPRC function calculates call prices for European options on futures, based on the Black model. The function is based on the following relationship:
table with 1 row and 1 column , row1 column 1 , c eh l l , equals . epsilon super negative r t end super . open f n . open , d sub 1 , close . minus e n . open , d sub 2 , close . close , end table
Arguments
F
specifies future price.
N
specifies the cumulative normal density function.
E
specifies the exercise price of the option.
r
specifies the risk-free interest rate, which is an annual rate that is expressed in terms of continuous compounding.
t
specifies the time to expiration, in years.
table with 2 rows and 2 columns , row1 column 1 , d sub 1 , equals , column 2 fraction open natural log of . open , f over e , close . plus . open , 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:
sigma
specifies the volatility of the underlying asset.
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 f 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 BLACKCLPRC function calculates call prices for European options on futures, based on the Black model. The BLACKPTPRC function calculates put prices for European options on futures, based on the Black model. These functions return a scalar value.

Example

The following statements illustrate the BLACKCLPRC function:
Statements
Results 
----+----1----+-—-2--
 
select blackclprc(50,.25,48,.05,.25);
 
1.55130142723117

select blackclprc(9,1/12,10,.05,.2);
 
1

See Also

Functions:
BLACKPTPRC Function
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