numerical pricing of american options under a nonlinear black-scholes framework with mixed fractional brownian motion

Transaction costs significantly impact option pricing and trading strategies in financial markets‎. ‎this study investigates the valuation of american options under transaction costs‎, ‎modeled as a linear function of the underlying asset price‎. ‎to capture long-range dependence in asset returns‎, ‎the underlying dynamics are described by a mixed fractional brownian motion (fbm)‎. ‎the model incorporates dividend-paying stocks‎, ‎along with time-varying interest and dividend rates‎. ‎a compact finite difference scheme is developed to solve the resulting nonlinear black-scholes equation‎, ‎ensuring numerical stability and accuracy‎. ‎the proposed framework offers an efficient approach for pricing american options in realistic market conditions.