The expectations approach values an option as the present value of the expected payoff at expiration. This involves:

1. Calculating the expected payoff at expiration using risk-neutral probabilities
2. Discounting this expected payoff back to the present using the risk-free rate

The formula is: Option Value = PV[E(Payoff)] = E(Payoff) / (1 + r)^t

This approach is fundamental to binomial option pricing models and risk-neutral valuation frameworks.