Question

. You are given the following two sets of prices of European options as a function of the strike price, for a stock with S = 100. Assume that all options mature in 6 months,
and that the interest rate (continuously compounding, annualized) is 10%.
(1) p(90) = 4; p(100) = 9 1/8 ; p(110) = 16; p(120) = 25 3/4

(2) p(90) = 2 ¾ ; p(100) = 81/2 ; p(110) = 17; p(120) = 24

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 pro_ts and show how that
portfolio performs whatever the underlying price does