The article explores a new way to price American call options by using a modified Black–Scholes equation with a nonlinear volatility function. The researchers developed a numerical method that transforms the problem into a Gamma variational inequality, allowing for more accurate pricing. By applying a specific numerical scheme, they were able to effectively calculate option prices even with variable transaction costs. The study demonstrates the usefulness of this approach through computational examples, showing how it can improve option pricing in real-world scenarios.