# GARKHPTPRC Function

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

 Category: Financial

## Syntax

GARKHPTPRC(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 Rt 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 GARKHPTPRC function calculates the put prices for European options on stocks, based on the Garman-Kohlhagen model. The function is based on the following relationship:
$equation$
Arguments
S
specifies the spot currency price.
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.
$equation$
The following arguments apply to the preceding equation:
$equation$
specifies the volatility of the underlying asset.
$equation$
specifies the variance of the rate of return.
For the special case of t=0, the following equation is true:
$equation$
For information about the basics of pricing, see Using Pricing Functions.

## Comparisons

The GARKHPTPRC function calculates the put prices for European options on stocks, based on the Garman-Kohlhagen model. The GARKHCLPRC function calculates the call 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=garkhptprc(1000, .5, 950, 4, 4, 2);`
`72.102451281`
`b=garkhptprc(850, 1.2, 125, 5, 3, 1);`
`0.5917507981`
`c=garkhptprc(7500, .9, 950, 3, 2, 2);`
`416.33604902`
`d=garkhptprc(5000, -.5, 237, 3, 3, 2);`
`           0`