An equilibrium approach to pricing foreign currency options

The paper presents a modified version of the Garman‐Kohlhagen formula for pricing European currency options. The equilibrium approach deviates from the no‐arbitrage approach by allowing domestic and foreign interest rates and their dynamics to be determined endogenously in the model. By using the relations between exchange rate dynamics and the dynamics of interest rates, I provide a new characterisation of the relevant volatilities for European currency option pricing, which only depends on parameters describing the variability of the log‐exchange rate. The implications of the model for the valuation of American currency options and optimal exercise strategies are examined by applying numerical methods.