The pricing of currency options: A test of the Garman-Kohlhagen pricing model

Understanding and quantifying the risk resulting from exchange rate changes is a fundamental challenge faced by financial managers of multinational corporations. The adoption of a flexible exchange rate system following the collapse of the Bretton Woods system of pegged exchange rates over fifteen years ago has made this risk even more difficult to manage. Furthermore, this exchange rate risk has given rise to a search for more efficient ways to manage the effects of currency fluctuations. This in turn, has given rise to exchange traded currency options. The dissertation examined the best method of using historical exchange rate changes and/or implied exchange rate changes to predict future currency volatility to use in the pricing of foreign currency options. The model used in this paper to price currency options is the Garman-Kohlhagen model which is a derivative of the Black-Scholes model used to price stock options. The Garman-Kohlhagen model was applied to the six currencies trading on the Philadelphia Stock Exchange using daily data for the period February 28, 1983 to June 27, 1985. The data source for the option contracts was the Philadelphia Stock Exchange/Ohio State University data base. The data source for the spot exchange rates was Chemical Bank and for the foreign and domestic interest rates was Data Resources Inc. In general, the results of the test indicate that the Garman-Kohlhagen model has some underlying deficiencies. Furthermore, even if one assumes the model to correctly price currency options, there are no clear indications that any one method of estimating currency volatility can be drawn. In addition, these inefficiencies in the pricing of over the counter currency options can lead to arbitrage opportunities with exchange traded options