  A new framework for pricing the European currency option is developed in the
case where the spot exchange rate fellows a time-changed fractional Brownian
motion. An analytic formula for pricing European foreign currency option is
proposed by a mean self-financing delta-hedging argument in a discrete time
setting. The minimal price of a currency option under transaction costs is
obtained as time-step $\Delta
t=\left(\frac{t^{\beta-1}}{\Gamma(\beta)}\right)^{-1}\left(\frac{2}{\pi}\right)^{\frac{1}{2H}}\left(\frac{\alpha}{\sigma}\right)^{\frac{1}{H}}$
, which can be used as the actual price of an option. In addition, we also show
that time-step and long-range dependence have a significant impact on option
pricing.
