1. (40 marks) Consider a one-period model (a period is one year) formed by a bond paying a risk-free rate of 4% per year, and by Stocks 1 and 2 with initial prices so = 7.8 and s = 7, respectively, and Si (wi) = 18, S1 (W2) = 15, S/(W3) = 3 and S? (wi) = 10, S (W2) = 8, S}(W3) = 6, with probabilities Pw1), P(w2), PW3) > 0 and PW1) + P(W2) + PW3) = 1. (a) (10 marks) Is the market free of arbitrage? (You need to give your reason.) (b) (10 marks) Is the market complete? (You need to give your reason.) (c) (10 marks) Consider a contingent claim X with contract function X = Q(S1, S3) { = max S - S +4 2 Find a fair price for X at time 0, i.e., II(0; X). (d) (10 marks) Find a replicating portfolio for X defined in (c). 1. (40 marks) Consider a one-period model (a period is one year) formed by a bond paying a risk-free rate of 4% per year, and by Stocks 1 and 2 with initial prices so = 7.8 and s = 7, respectively, and Si (wi) = 18, S1 (W2) = 15, S/(W3) = 3 and S? (wi) = 10, S (W2) = 8, S}(W3) = 6, with probabilities Pw1), P(w2), PW3) > 0 and PW1) + P(W2) + PW3) = 1. (a) (10 marks) Is the market free of arbitrage? (You need to give your reason.) (b) (10 marks) Is the market complete? (You need to give your reason.) (c) (10 marks) Consider a contingent claim X with contract function X = Q(S1, S3) { = max S - S +4 2 Find a fair price for X at time 0, i.e., II(0; X). (d) (10 marks) Find a replicating portfolio for X defined in (c)