Currency option pricing in a credible exchange rate target zone

This article examines currency option pricing within a credible target zone arrangement where interventions at the boundaries push the exchange rate back into its fluctuation band. Valuation of such options is complicated by the requirement that the reflection mechanism should prevent the arbitrage opportunities that would arise if the exchange rate were to spend finite time on the boundaries. To prevent the latter, we superimpose instantaneously reflecting boundaries upon the familiar geometric Brownian motion (GBM) framework. We derive closed-form expressions for European call and put option prices and show that prices for the GBM model of Garman and Kohlhagen (1983) arise as the limit case for infinitely wide bands. We also illustrate that taking account of boundaries is of considerable economic value as erroneously using the unbounded-domain model of Garman and Kohlhagen (1983) easily overprices options by more than 100%.