Consider the probability space= {w, W2, W3], with the probability P such that P({w}) = 1/3 for every wen. Define the random variables Consider the one-period trinomial model of the market (B, S) made of a bond B with initial price 1 (all prices in a fixed currency, say ), and interest rate r = 1, a stock whose initial price is So 4, and whose final price is S. In the questions (a-e) we consider the market model (B, S), and the random variables X and Y represent the payoffs of two illiquid derivatives (with S as underlying); in question (f) Y represents instead the value at time 1 of a traded asset, which is part of the market model (B, S, Y). W1 W2 W3 S (w) 6 X(w) -6 8 10 4 14 Y(w) 16 6 2 (a) Is the market model (B, S) free of arbitrage? A. No B. Yes (b) Is X replicable? A. No B. Yes (c) Is Y replicable? A. No B. Yes (d) What is the set of arbitrage-free prices of X? A. (2,4) B. [2,4] C. {4} D. {2} E. None of the above (e) What is the set of arbitrage-free prices of Y? A. (3,9/2) B. (6,9) C. {3} D. {6} E. None of the above (f) Now enlarge the (B, S) market, by assuming that Y is traded at the arbitrage-free price Yo at time 0. If an illiquid derivative has a payoff Z which is not replicable using only bonds and stocks (i.e. Z is not replicable in the (B, S) market), does Z have a nique arbitr e-fre price in the market (B, A. Not enough info to answer (it depends on Z) B. No C. Yes