  Using a Levy process we generalize formulas in Bo et al.(2010) for the
Esscher transform parameters for the log-normal distribution which ensure the
martingale condition holds for the discounted foreign exchange rate. Using
these values of the parameters we find a risk-neural measure and provide new
formulas for the distribution of jumps, the mean jump size, and the Poisson
process intensity with respect to to this measure. The formulas for a European
call foreign exchange option are also derived. We apply these formulas to the
case of the log-double exponential distribution of jumps. We provide numerical
simulations for the European call foreign exchange option prices with different
parameters.
