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

Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs