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.
Babaei, A. and Rezaei, M. (2025). Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion. Journal of Mathematical Modeling, (), -. doi: 10.22124/jmm.2025.30891.2773
MLA
Babaei, A. , and Rezaei, M. . "Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion", Journal of Mathematical Modeling, , , 2025, -. doi: 10.22124/jmm.2025.30891.2773
HARVARD
Babaei, A., Rezaei, M. (2025). 'Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion', Journal of Mathematical Modeling, (), pp. -. doi: 10.22124/jmm.2025.30891.2773
CHICAGO
A. Babaei and M. Rezaei, "Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion," Journal of Mathematical Modeling, (2025): -, doi: 10.22124/jmm.2025.30891.2773
VANCOUVER
Babaei, A., Rezaei, M. Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion. Journal of Mathematical Modeling, 2025; (): -. doi: 10.22124/jmm.2025.30891.2773
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