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Consider a multi-period market model M = (B; S) with two assets: the savings account B and the risky asset S. For a natural number T, consider the following model for the price of the risky asset S :

St = S0 + Y1 + Y2 + + Yt ;

where the random variables Y1, . . . , YT are independent and identically distributed under the real-world probability measure P, specifically, P(Y1 = +a) = 0.25; P(Y1 = -a) = 0.75

where a > 0 is a strictly positive constant. We assume that the risk-free rate r = 0 so that the savings account equals Bt = 1 for every t = 0; 1; T. (a) Check whether the model M = (B; S) is arbitrage-free and complete. (b) Find the option price process t(X), t = 0; 1; 2; 3 and the replicating strategy = (0 1) for the claim X = max(0S3-S1) maturing at time T = 3