Under the risk-neutral measure Q, the expected return on all assets equals the risk-free rate r. In the binomial model: p* = (e^(rΔt) − d)/(u − d). Option price = e^(−rT) × E^Q[payoff at expiry]. Risk-neutral probabilities are NOT real-world probabilities — they are mathematical tools that capture market risk aversion and allow pricing by expectation. The connection to real probabilities requires specifying the market price of risk (risk premium).