Currency option pricing with mean reversion and uncovered interest parity: A revision of the Garman-Kohlhagen model

Abstract

We consider a model for the pricing of currency options where the logarithm of the exchange rate exhibits mean reversion, i.e. follows the Omstein-Uhlenbeck process. We mention reasons why exchange rates could exhibit mean reversion. The domestic and foreign short interest rates are related to the logarithm of the exchange rate through Uncovered Interest Parity. Under these assumptions, we derive formulas for the value of a European currency option, from the point of view of both domestic and foreign investors. We also derive formulas for options on forward and futures contracts. We compare option values computed by means of the Garman-Kohlhagen model with corresponding results from our model. It appears that our model cannot explain all instances of mispricing of currency options by the Garman-Kohlhagen model which have been reported by previous authors. The main virtue of our paper, however, is that we derive a simple model which incorporates clear theoretical relationship between the exchange rate and the domestic and foreign interest rates.