The price of a non-dividend-paying stock is $100 per share now. The price of a 6-month European put option on this stock with a strike price of $105 Is $7.5 now. The risk free rate is always 3% per annum with continuous compounding. (a) Consider a 6-month European call option on this stock with a strike price of $105. What is the price of this 6-month European call option now? (b) If the price of the 6-month European call option in (a) is $5 now, what is the arbitrage opportunity? Provide your strategy in detail. wwwwww (c) Consider a 6-month derivative security whose payoff at maturity is the maximum of ST-97 and 113-ST, i.e., max (ST-97, 113-ST), where T denotes the maturity (6 months) and ST is the stock price at maturity. This derivative security cannot be exercised early. What is the price of this derivative security now? Question 1 [20 marks] Consider the payoff matrix 1.1 4 3 and the price vector 1.1 3 2 A = = 1.1 0 0 1.1 1 0 1.05 S = 2 1.5 a. Is the market complete? b. What is the return of the risk-free asset? c. Find state prices consistent with A and S and the Law of One Price, and then determine whether there is arbitrage. d. If there is arbitrage, propose an arbitrage portfolio and explain what type of arbitrage it is. If there is no arbitrage, state what the risk- neutral probabilities are. 1. Consider a general one-period asset pricing model with the following information: := {11, 12, 13} S1(0) = 5, S2(0) = 10, r = 0.2. S(1, w) = 2, S(1, 2) = 6, S1(1, 3) = 7. S2(1, 1) = 6, S2(1, w2) = 8, S2(1, 3) = 15. 1) If derivative X with time 1 payoff X(1, w;) = S2(1, w;) - S(1, w;), w; S2, compute the price of X at time 0 with the risk-free asset and the two risky assets S1 and S2. 2) Is the market arbitrage free? Is the market complete?