The Garman and Kohlhagen Model versus a Currency Option Pricing Model with Stochastic Interest Rates and Transaction Costs

In this paper, we develop and test a currency option pricing model with stochastic interest rates and transactions costs when interest parity holds, and it is assumed that domestic and foreign bond prices have local variances that depend only on time. These additional parameters are introduced in a very simple way, through an adjustment of the volatility in the Grabbe currency option pricing model. The ‘pure’ Garman and Kohlhagen strategy holds only in the limiting case of constant interest rates and zero transactions costs. We test our theoretical model employing transactions data for European currency call options traded on the Philadelphia Stock Exchange. The historical standard deviation are used as the estimators of future volatility of exchange rates. In both cases, the Garman and Kohlhagen model in average performs better than other models with stochastic interest rates and/or transaction costs.