The transaction costs to buyers and sellers in financial market are the payments that banks, brokers, and agent receive for their roles in connecting buyers and sellers. The fees paid to a brokerage for executing an option trade are a transaction cost. Hence, transaction cost is an influential issue in the financial market and institutions that facilitate low transaction costs, boost economic growth. Since the underlying asset in the option has a transaction cost, the option is also affected by the transaction cost. In this manuscript, we consider the American option pricing with transaction cost as a linear function. On the other hand, empirical studies show long-range dependence in the financial market. Thus, we assume that the underlying asset price in this option follows the mixed fractional Brownian motion model with Hurst parameter H to show the long-range dependence property. We assume that stocks pay dividends and also that the parameters of interest rate and dividend yield are time dependent. We consider a compact difference scheme for numerical pricing the American option.
