One way to model an option with dividends in the binomial framework is for the stock price minus the present value of the dividends to grow by the up and down factors.

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This is the correct way to model an option with dividends in the binomial framework. The present value of the dividends is subtracted from the stock price to take into account the fact that the holder of the option will not receive these payments.

One Way to Model an Option with Dividends in the Binomial