What Is the Primary Mathematical Model Used to Price American Options, and Why Is It More Complex than the Black-Scholes Model?

The primary model used for American options is the Binomial Option Pricing Model or its continuous-time equivalent, the Black-Scholes model with an adjustment for early exercise, often solved using numerical methods like finite difference or Monte Carlo simulations. Black-Scholes assumes European-style exercise, making it unsuitable for American options.

The complexity arises from the need to evaluate the optimal early exercise decision at every point in time before expiration.