Abstract: Assuming that the exchange rate fllows jump fractional Brownian motion,by constructing foreign currency option market under jump fractional Brownian environment,a pricing formula for a European contingent claim is derived by using fractional Girsanov formula and self-financing strategy.Moreover,a pricing formula of a European foreign currency option is obtained based on the principle of option pricing.At last,we give an empirical analysis of EUR/USD option,the results of different pricing models show that foreign currency market has both jump and fractal properties.

Key words: foreign currency options, fractional brownian motion, fractional-Ito-Integration, pricing model