MARGRCLPRC Function

Calculates call prices for European options on stocks, based on the Margrabe model.

Category: Financial

Syntax

MARGRCLPRC(X1, t, X2, sigma1, sigma2, rho12)

Required Arguments

X1

is a nonmissing, positive value that specifies the price of the first asset.

Requirement Specify X1 and X2 in the same units.

t

is a nonmissing value that specifies the time to expiration.

X2

is a nonmissing, positive value that specifies the price of the second asset.

Requirement Specify X2 and X1 in the same units.

sigma1

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

Requirement sigma1 must be for the same time period as the unit of t.

sigma2

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

Requirement Specify a value for sigma2 for the same time period as the unit of t.

rho12

specifies the correlation between the first and second assets, ρ x 1 x 2 .

Range between –1 and 1

Details

The MARGRCLPRC function calculates the call price for European options on stocks, based on the Margrabe model. The function is based on the following relationship:
C A L L = X 1 N ( d 1 ) - X 2 N ( d 2 )
Arguments
X1
specifies the price of the first asset.
X2
specifies the price of the second asset.
N
specifies the cumulative normal density function.
d 1 = ( ln ⁡ ( N 1 N 2 ) + ( σ 2 2 ) t ) σ t d 2 = d 1 - σ t σ 2 = σ x 1 2 + σ x 2 2 - 2 ρ x 1 , x 2 σ x 1 σ x 2
The following arguments apply to the preceding equation:
t
specifies the time to expiration.
σ x 1 2
specifies the variance of the first asset.
σ x 2 2
specifies the variance of the second asset.
σ x 1
specifies the volatility of the first asset.
σ x 2
specifies the volatility of the second asset.
ρ x 1 , x 2
specifies the correlation between the first and second assets.
For the special case of t=0, the following equation is true:
C A L L = max ⁡ ( ( X 1 - X 2 ) , 0 )
Note: This function assumes that there are no dividends from the two assets.
For information about the basics of pricing, see Using Pricing Functions.

Comparisons

The MARGRCLPRC function calculates the call price for European options on stocks, based on the Margrabe model. The MARGRPTPRC function calculates the put price for European options on stocks, based on the Margrabe model. These functions return a scalar value.

Example

The following SAS statements produce these results.
SAS Statement
Result 
----+----1----+-—-2--
 
a=margrclprc(500, .5, 950, 4, 5, 1);
put a;
 
46.441283642
 
b=margrclprc(850, 1.2, 125, 5, 3, 1);
put b;
 
777.67008185
 
c=margrclprc(7500, .9, 950, 3, 2, 1);
put c;
 
6562.0354886
 
d=margrclprc(5000, -.5, 237, 3, 3, 1);
put d;
 
           0

See Also

Functions:
MARGRPTPRC Function
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