American options pricing under mixed fractional Brownian motion model with transaction costs

In economics and financial mathematics, a transaction cost is a cost in making any economic trade when participating in a market. So, 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 an implicit difference scheme for numerical pricing the American option. Finally, we present some numerical results for the correctness of the proposed method.

کلیدواژه ها:

American options ، Fractional Brownian motion ، Transaction costs ، Difference scheme