Consider an economy with three possible states of the world and three traded securities (i.e., \(S=N=3\) ), with price-dividend couple

\[D=\left[\begin{array}{ccc}2 & 3 & 2 \\2 & 3 & 5 \\5 & 4 / 3 & 3\end{array}\right] \quad \text { and } \quad\left(\begin{array}{l}6 \\4 \\k\end{array}\right)\]

(i) Determine the values of \(k\) for which there are no arbitrage opportunities in the market.

(ii) Determine the range of arbitrage free prices for a Call option written on the first security with strike price 3 .

(iii) For a fixed value of \(k\) such that arbitrage opportunities are present in the market, construct a portfolio which is an arbitrage opportunity.