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This paper deals with the problem of discrete-time option pricing by themixed fractional version of Merton model with transaction costs. By amean-self-financing delta hedging argument in a discrete-time setting, aEuropean call option pricing formula is obtained. We also investigate theeffect of the time-step $\delta t$ and the Hurst parameter $H$ on our pricingoption model, which reveals that these parameters have high impact on optionpricing. The properties of this model are also explained.

The valuation of European option with transaction costs by mixed fractional Merton model