GARKHCLPRC Function

Calculates call prices for European options on stocks, based on the Garman-Kohlhagen model.

Category: Financial

Syntax

GARKHCLPRC(E, t, S, Rd, Rf, 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 spot currency price.

Requirement Specify S and E in the same units.

Rd

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

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

Rf

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

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

sigma

is a nonmissing, positive fraction that specifies the volatility of the currency rate.

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

Details

The GARKHCLPRC function calculates the call prices for European options on stocks, based on the Garman-Kohlhagen model. The function is based on the following relationship:
C A L L = S N ( d 1 ) ( ε - R f t ) - E N ( d 2 ) ( ε - R d t )
Arguments
S
specifies the spot currency price.
N
specifies the cumulative normal density function.
E
specifies the exercise price of the option.
t
specifies the time to expiration.
Rd
specifies the risk-free domestic interest rate for period t.
Rf
specifies the risk-free foreign interest rate for period t.
d 1 = ( ln ⁡ ( S E ) + ( R d - R f + σ 2 2 ) t ) σ t d 2 = d 1 - σ t
The following arguments apply to the preceding equation:
σ
specifies the volatility of the underlying asset.
σ 2
specifies the variance of the rate of return.
For the special case of t=0, the following equation is true:
C A L L = max ⁡ ( ( S - E ) , 0 )
For information about the basics of pricing, see Using Pricing Functions.

Comparisons

The GARKHCLPRC function calculates the call prices for European options on stocks, based on the Garman-Kohlhagen model. The GARKHPTPRC function calculates the put prices for European options on stocks, based on the Garman-Kohlhagen model. These functions return a scalar value.

Example

The following SAS statements produce these results.
SAS Statement
Result 
----+----1----+-—-2--
 
a=garkhclprc(1000, .5, 950, 4, 4, 2);
put a;
 
65.335687119
 
b=garkhclprc(850, 1.2, 125, 5, 3, 1);
put b;
 
1.9002767538
 
c=garkhclprc(7500, .9, 950, 3, 2, 2);
put c;
 
69.328647279
 
d=garkhclprc(5000, -.5, 237, 3, 3, 2);
put d;
 
           0

See Also

Functions:
GARKHPTPRC Function
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