1. 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,

Question

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.

(b) Would your answer to Part (a) change if these put options are Americans? Why?

(c) Would your answer to Part (a) change if the stock will pay an unknown amount
of dividend in 3 months? Explain why.