Explanation

The correct answer is A: The binomial option valuation model only.

Key differences between the models:

Binomial Option Valuation Model

• Can value American options because it allows for early exercise at each node
• Works by building a price tree and evaluating exercise decisions at each time step
• Can incorporate the possibility of early exercise when it's optimal

Black–Scholes–Merton (BSM) Model

• Cannot value American options directly
• Assumes European-style options (no early exercise)
• Closed-form solution that doesn't account for early exercise opportunities
• Primarily used for European options

Why BSM doesn't work for American options:

• American options can be exercised at any time before expiration
• Early exercise may be optimal when the option is deep in-the-money or when there are dividends
• BSM assumes continuous trading and no early exercise

Alternative approaches for American options:

• Binomial/trinomial trees
• Finite difference methods
• Monte Carlo simulation with early exercise features

Therefore, only the binomial model among the given choices is appropriate for valuing American options.