Pricing Currency Options under Stochastic Interest Rates and Jump-Diffusion Processes

We investigate the effects of stochastic interest rates and jumps in the spot exchange rate on the pricing of currency futures, forward and futures options. The proposed model extends Bates's model by allowing both the domestic and foreign interest rates to move around randomly, in a generalized Vasicek term structure framework. Numerical examples show that the model prices of European currency futures options are similar to those given by Bates's and Black's models in the absence of jumps and when the volatilities of the domestic and foreign interest rates and futures price are negligible. Changes in these volatilities affect the futures options prices. Both Bates's and Black's models underprice the European currency futures options in the presence as well as in the absence of jumps. The mispricing increases with the volatilities of interest rates and futures price.