Garman-Kohlhagen Option Pricing Model Applications and Uses

Employ Garman-Kohlhagen option pricing model applications and uses to improve capital management

The Garman-Kohlhagen option formula is a variation on the Black Scholes model but it denotes foreign and domestic interest rates as separate terms. The primary use for the Garman-Kohlhagen pricing model is for put and calls foreign currency options. However, you can use this formula for dynamic hedging of your currency risks. While the Garman-Kohlhagen option pricing model applications and uses are narrow in scope, learning those uses are not.

The Garman-Kohlhagen options put formula differs slightly from the one for a foreign currency call options. When using this formula you must assume that transaction costs and taxes are zero, the distribution of the currency exchange rate is lognormal, arbitrage isn't a possibility, the foreign rates, risk-free rates and currency exchange rate volatility are known over the life of the option and there are no penalties for short sales. Once you make these assumptions, then you can use the Garman-Kohlhagen option valuation model for the following:

1. Use the Garman-Kohlhagen option pricing model information to price a foreign currency call option.

2. Calculate the price of foreign currency put option with the Garman-Kohlhagen option model.

3. Utilize the Garman-Kohlhagen pricing formula for dynamic hedging.

Price a call foreign currency option with Garman-Kohlhagen option pricing information

The put foreign currency option pricing models for Garman-Kohlhagen option is as follows: c = S\exp(-r_f T)\N(d_1) - K\exp(-r_d T)\N(d_2) In this formula, rf is foreign risk free rate, N is the cumulative normal distribution function, S is the spot currency rate, K is the strike rate, rd is the risk free rate, and s is the volatility of the FX rate. To price a call option you'll need to obtain the inputs for all of the above variables.

Obtain the put option price using the Garman-Kohlhagen option valuation model

To attain the correct pricing for a put currency option you use a slight variation on the call option Garman-Kohlhagen pricing formula. To make it easier you swap the aforementioned sides of the formula to read as follows: p = K\exp(-r_d T)\N(-d_2) - S\exp(-r_f T)\N(-d_1). The variable definitions for the formula remain the same.

Apply the Garman-Kohlhagen option formula in a dynamic hedging strategy

Dynamic hedging is when you use an underlying security to limit the risk of the primary security. For instance, in derivatives trading you can price a foreign currency option with the formula, then purchase a short option to offset the risk by purchasing a linear position in the same currency.

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