Consider a market model with two assets: one risk-free asset whose price process A(0) = 1 and A(1) = 1+r and the risky asset whose price is given by S(0) and S(1) takes three values S(0)U, S(0)M and S(0)D, where D < M < U. a) Determine the equations that any risk-neutral probability Z = (Z1,Z2,Z3) for this model should fullfil. b) Prove that the model admits no arbitrage if and only if D < 1 + r < U: c) Give two risk-neutral probabilities for the model such that one of their entries is zero (discuss cases whether M is smaller than 1 + r or not) (here we relax the assumption of all the entries of a risk neutral measure should be positive in the definition of a risk-neutral measure. That is the entries may be zero but non-negatives and add up to one). d) Consider a call option with strike price K satisfying S(0)M < K < S(0)U. Calculate the expected value of the discounted price of the call at time t = 1 under the measures obtained in question c). e) Prove that the highest value and the lowest value obtained in d) coincide when M = D. Problem 3 Consider the model constituted by three securities. The bank account whose price process is A(0) = A(1) = A(2) = 1, and two stocks with the pric