Jump-diffusion processes and general equilibrium in pricing foreign currency option

Abstract

This paper derives explicit formulas for European foreign exchange call and put option values when the exchange rate dynamics are governed by jump-diffusion processes. We have used a simple general equilibrium international asset pricing model with continuous trading and frictionless international capital markets. The domestic and foreign price level are introduced as state variables which contain jumps initiated by government's monetary policy. The domestic and foreign interest rates are stochastic and endogenously determined in the model and are shown to be critically affected by jump risk of the foreign exchange. The model shows that the behavior of FX options is affected through impacts of state variables and parameters on the nominal interest rates. The model contrasts with those of Garman and Kohlhagen (1983) and Grabbe (1983) which have exogenously determined interest rates.