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We deal with options pricing at work. Binomial isn't a tough concept once you conceptually what you're doing. It's essentially a tree that maps the likelihood that a stock price will go up or down. Since there are only 2 possible options, up or down, 1 - probability up = probability down and vice versa. Essentially, your getting confused by the transposition of the problem.

In reality, the binomial is too general to give you and accurate view of the pricing. Trinomial models take into account the probability that the stock price will remain the same and more complex models, like the Gram-Charlier model take into account skewness and kurtosis.

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