Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion

Document Type : Research Article

Authors

1 Faculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran.

2 Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

Abstract

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.

Keywords

Main Subjects


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