This paper investigates two nonlinear Black-Scholes models, which are fundamental in options pricing under conditions where market volatility is non-constant. To address the inherent complexity in these models, a regime-switching approach is employed, decomposing each model into a system of differential equations, with each equation representing a distinct market regime. Leveraging Lie group algebra, we derive exact analytical solutions for the equations within this system, providing critical insights into the model dynamics under various regimes. Numerical solutions are obtained using the Chebyshev spectral method, a high-precision approach known for its efficiency in solving differential equations to complement the analytical results.