University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion 557 577 9245 10.22124/jmm.2025.30891.2773 EN Afshin Babaei Faculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran. Maryam Rezaei Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. Journal Article 2025 06 05 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. https://jmm.guilan.ac.ir/article_9245_9a406f97ece14eddc4d6d2bf17bca9b5.pdf