What Are the Limitations of the Black-Scholes Model When Attempting to Price American Options?

The Black-Scholes model is a closed-form solution that assumes the option can only be exercised at expiration, which violates the key feature of an American option. Therefore, the BSM model cannot accurately account for the added value and complexity of the early exercise feature.

More complex numerical methods, like the binomial model, are required for accurate American option pricing.