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.
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