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Risk-Neutral Valuation

bionicml

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In Chapter 4 Binomial Trees of the book Valuation and Risk Models, under "Irrelevance of the Stock's Expected Return," it says "The option pricing formula in Equation (4.2) does not involve the probabilities of the stock price moving up or down. "
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However, on the same page, under "Risk-Neutral Valuation," it says "Returning to Equation (4.2), the parameter p should be interpreted as the probability of an up movement in a risk- neutral world, so that 1 - p is the probability of a down movement in this world. "

How should I understand the seemingly contradictory statements here?
Thank you!
 
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