Does the Early Exercise Feature Affect the Pricing Model, Such as Black-Scholes, for American Options?

Yes, the early exercise feature fundamentally changes the pricing model. The standard Black-Scholes model is designed for European options and does not account for the possibility of early exercise.

More complex models, such as the binomial model or finite difference methods, are required to accurately price American options, as they must incorporate the optimal decision to exercise at every point in time.