Suppose that Ω = {ω1, ω2, ω3}. Assume that P is a probability measure on Ω such that P(w) > 0 for all ω ∈ Ω. Let S0 be a constant representing the value of a stock at time 0 and let S1 be a random variable on Ω representing the value of the stock at time 1. This is a one-period trinomial model. The only difference with the one-period binomial model is that there are three possible states of the world (all occurring with positive probability) instead of only two (as we have in the binomial model). Suppose that S0 = 100, S1(ω1) = 120, S1(ω2) = 100, S1(ω3) = 80, and that there exists a money market account with constant interest rate r = 0.1. Describe the set M of all risk-neutral P-equivalent probability measures, i. e. the set of all probability measures P˜ on Ω such that P˜(ω) > 0 for all ω ∈ Ω and E˜ [S1] = S0, where E˜ denotes the expectation with respect to P˜. ♦2. Using the fact that M is not empty, prove that this model is free of arbitrage. Why is it important to have P˜(ω) > 0 for all ω ∈ Ω as a property of the risk-neutral measures? ♦3. Is it possible to replicate any contingent claim in this model? Justify your answer. ♦4. Suppose that V1 is a contingent claim that can be replicated by trading in S and in the money market account with initial capital V0. Show that E˜[V1] = V0, for any measure P˜ ∈ M. Is the replication strategy for V1 (i. e. initial capital and initial position on S) unique?