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I believe the Binomial model is better then black scholes model for options pricing. Although Black Scholes is much quicker and easier to calculate, the Binomial Model's main advantage is that it allows checking the possibility of early exercise at every point of an options life. This is particularly very important for American options as they can be exercised at any time during their life.
Therefore, the binomial tree would allow you to calculate if a call or put Is deep in the money and allow for early exercise in the case of American options.
