GARKHPTPRC Function

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

Category:

Financial

Syntax

GARKHPTPRC(E, t, S, R_d, R_f, 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.

R_d

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

Requirement

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

R_f

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

Requirement

Specify a value for R_t 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:

\begin{matrix} P U T = C A L L - S (ε \begin{matrix} - R_{f^{t}} \end{matrix}) + E (ε \begin{matrix} - R_{d^{t}} \end{matrix}) \end{matrix}

Arguments

specifies the spot currency price.

specifies the exercise price of the option.

specifies the time to expiration.

R_d

specifies the risk-free domestic interest rate for period t.

R_f

specifies the risk-free foreign interest rate for period t.

\begin{matrix} d_{1} = & \frac{(\ln (\frac{S}{E}) + (R_{d} - R_{f} + \frac{σ^{2}}{2}) t)}{σ \sqrt[]{t}} \\ d_{2} = & d_{1} - σ \sqrt[]{t} \end{matrix}

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:

\begin{matrix} P U T = \max ((E - S), 0) \end{matrix}

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

GARKHPTPRC Function

Syntax

Required Arguments

E

t

S

Rd

Rf

sigma

Details

Comparisons

Example

See Also

R_d

R_f