You are given the following three sets of prices of European options (for the given strikes). In each case the underlying stock (which does not pay divi- dends) is priced at S = 100. Assume that all options mature in 6 months, and that the interest rate (continuously compounding, annualized) is 10%. (1) p(90) p(100) = p(110) = 16 p(120) 25 = (2) 314112 p(90) 2/ p(100) = 8/3/2 p(110) = 17 p(120) = 24 (3) c(90) = 17.10 p(90) = 2.71 c(100) = 8.95 p(100) = 5.05 For each set of prices, please answer the following questions: (a) Assume that the stock will not pay any dividend in the next 6 months. Do these prices satisfy arbitrage restrictions on options values? If yes, prove it. If not, construct an arbitrage portfolio to realize riskless prof- its, and show how that portfolio performs under different market con- ditions. (E.g., you could use an arbitrage table.) (b) Would your answer to Part (a) change if these put options are Ameri- cans? Very briefly explain why. (c) Do your answers to parts (a) or (b) change if the stock will pay a $1 dividend in 3 months? Very briefly explain why.