MARGRCLPRC Function

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

Category:	Financial
Returned data type:	DOUBLE

Syntax

Syntax

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

Arguments

X₁

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

Requirement	Specify X₁ and X₂ in the same units.
Data type	DOUBLE

t

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

Data type

DOUBLE

X₂

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

Requirement	Specify X₂ and X₁ in the same units.
Data type	DOUBLE

sigma1

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

Data type

DOUBLE

sigma2

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

Data type

DOUBLE

rho12

specifies the correlation between the first and second assets, .

Range	between –1 and 1
Data type	DOUBLE

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:

table with 1 row and 1 column , row1 column 1 , c eh l l , equals , x sub 1 n . open , d sub 1 , close . minus , x sub 2 n . open , d sub 2 , close , end table

Arguments

X₁

specifies the price of the first asset.

X₂

specifies the price of the second asset.

specifies the cumulative normal density function.

$table with 3 rows and 2 columns , row1 column 1 , , column 2 d sub 1 , equals . fraction open natural log of . open . fraction n sub 1 , over n sub 2 end fraction . close . plus . open , fraction sigma squared , over 2 end fraction , close . t close , over sigma square root of t end fraction , row2 column 1 , , column 2 d sub 2 , equals , d sub 1 , minus sigma square root of t , row3 column 1 , , column 2 sigma squared , equals . sigma with subscript x sub 1 , and with superscript 2 , end sub-superscript . plus . sigma with subscript x sub 2 , and with superscript 2 , end sub-superscript . negative 2 rho sub x sub 1 , sub comma end sub , x sub 2 end sub . sigma sub x sub 1 end sub . sigma sub x sub 2 end sub , end table$

The following arguments apply to the preceding equation:

specifies the time to expiration.

sigma with subscript x sub 1 , and with superscript 2 , end sub-superscript

specifies the variance of the first asset.

sigma with subscript x sub 2 , and with superscript 2 , end sub-superscript

specifies the variance of the second asset.

specifies the volatility of the first asset.

specifies the volatility of the second asset.

rho sub x sub 1 comma end sub . x sub 2 end sub

specifies the correlation between the first and second assets.

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 , x sub 1 , minus , x sub 2 , close . comma 0 close , end table

Note: This function assumes that there are no dividends from the two assets.

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

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 statements illustrate the MARGRCLPRC function:

Statements	Results
select margrclprc(15, .5, 13, .06, .05, 1); put a;	2
select margrclprc(2, .25, 1, .3, .2, 1); put b;	1

MARGRCLPRC Function

Syntax

Arguments

X1

t

X2

sigma1

sigma2

rho12

Details

Comparisons

Example

See Also

X₁

X₂